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  • Articles  (1,121)
  • Other Sources
  • Wiley-Blackwell  (1,121)
  • Annual Reviews
  • 1980-1984  (1,121)
  • 1935-1939
  • Mathematics  (1,121)
  • 1
    Electronic Resource
    Electronic Resource
    Masthead (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020301
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  • 2
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    Über das Verhalten der Lösungen der Maxwellschen Randwertaufgabe in Gebieten mit Kegelspitzen (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 235-250 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the behavior of the solution E of the Maxwell's boundary value problem ∇ × ∇ × E + λE = F, n × E|r = 0 in domains Ω which have conical boundary points. In a neighbourhood K(R) = B(a,R) ∩ Ω of a singular boundary point a the field E is expanded using a theorem of N. Weck. It e.g. turns out that the solution lies in H1(3)(K(R)) if K(R) is convex.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020209
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  • 3
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    Eigenvalue bounds for Hill's equationThis work was performed under the terms of the agreement on association between Max-Planck-Institut for Plasmaphysik and EURATOM. (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 288-302 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For Hill's equation the lowest eigenvalue a0 of the boundary value problem y(x + 1) = y(x) is considered. Introducing Lp norms of the function f(x), lower bounds for a0 which depend only on this norm are derived for p = 1,2 and ∞ by solving a variational principle. For these lower bounds analytical expressions are obtained. The quality of the approximations thus obtained is discussed for Mathieu's equation and an application in magnetohydrodynamics is considered.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020304
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  • 4
    Electronic Resource
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    A local compactness theorem for Maxwell's equations (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 12-25 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper gives a proof, valid for a large class of bounded domains, of the following compactness statements: Let G be a bounded domain, β be a tensor-valued function on G satisfying certain restrictions, and let {n} be a sequence of vector-valued functions on G where the L2-norms of {n}, {curl n}, and {div(β n)} are bounded, and where all n either satisfy x n = 0 or (β Fn) = 0 at the boundary ∂G of G ( = normal to ∂G): then {n} has a L2-convergent subsequence. The first boundary condition is satisfied by electric fields, the second one by magnetic fields at a perfectly conducting boundary ∂G if β is interpreted as electric dielectricity ∊ or as magnetic permeability μ, respectively.These compactness statements are essential for the application of abstract scattering theory to the boundary value problem for Maxwell's equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020103
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  • 5
    Electronic Resource
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    Gradient bounds for plasma confinement (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 68-72 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of plasma confinement in a Tokomak machine has recently attracted considerable mathematical attention. In the present article, gradient bounds for the solution are obtained through the use of differential inequalities and the Hopf maximum principle. These estimates, which take slightly different forms in the plasma and vacuum regions, become exact in the one-dimensional case. An estimate is also given for the distance from the boundary of the interior point where the maximum of the solution is attained.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670020107
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  • 6
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    Differentiable dependence upon the data in a one-phase Stefan problem (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 73-90 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is well known that the free boundary of the one-phase Stefan problem (1.1-5) depends continuously on the boundary data [1]. In this paper we prove that, in addition, the solution operator S which, to each g. assigns the corresponding free boundary, is continuously Frechet differentiable and we give the defining formulas of the Frechet derivative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020108
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  • 7
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    Über die Radon-Transformation kreissymmetrischer Funktionen und ihre Beziehung zur Sommerfeldschen Theorie der Hankelfunktionen (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 108-129 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For the Radon transform of functions with circular symmetry an inversion formula is proved in a new and elementary way. The inversion formula combined with Fourier theory is applied to Sommer-feld's integral for Hv1, yielding a representation of products which generalizes Nicholson's integral for |Hv(1)| 2.
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    URL: http://dx.doi.org/10.1002/mma.1670020110
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  • 8
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    A finite element method for the double-layer potential solutions of the Neumann exterior problem (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 191-208 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A variational formulation for the integral equation used for the double layer potential solution of the Neumann exterior problem in the Laplace equation was proposed in [4]. This formulation allows the use of a finite element method which we describe and experiment here.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670020206
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  • 9
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    Uniform convergence of the horizontal line method for solutions and free boundaries in Stefan evolution inequalities (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 149-167 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The change of variable for the temperature Θ in the one-phase Stefan problem leads to the evolution inequality, (ut - Δu - f)(v - u) ≥ 0 for all regular v ≥ 0, where u ≥ 0 is required. This inequality is to hold over a space-time domain D = Ω × (0, T) with a Dirichlet boundary condition imposed on ∂ Ω × (0, T) and a zero initial condition. The free boundary phase interface is given in one space dimension by The fully implicit divided difference scheme leads to a sequence of elliptic variational inequalities for {um}. The sequence {um} may be interpolated linearly in t to obtain an approximation UΔt of u. The following results are obtained in this paper: (i) a two-sided weak maximum principle for um - um-1 in N space dimensions, hence the free boundary approximation for N = 1, is a monotone increasing step function; (ii) the uniform convergence of UΔt and ∇UΔt, to u and ∇u, respectively, on D; (iii) the uniform convergence to the Hölder continuous, monotone increasing free boundary x on [0, T] of the piecewise linear sequence xΔt, where xΔt interpolates xΔt, in one space dimension; (iv) a constructive existence proof for u and x in prescribed regularity classes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020203
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  • 10
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    Picture reconstruction from projections in restricted range (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 209-220 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In order to reduce scanning time modern x-ray scanners provide projections only in a restricted range [0, φ] with φ 〈 π. We consider the reconstruction of pictures from p + 1 complete projections in [0, φ]. An extrapolation procedure is given to achieve approximations gp of the data in the whole range. We show that the L2-error of the corresponding picture is of order p-α if the original belongs to the Sobolev space Hoα. The validity of our error estimate is investigated by numerical experiments.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670020207
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  • 11
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    The effect of a thin inclusion of high rigidity in an elastic body (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 251-270 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study an elastic body comprising an inclusion whose thickness is 2∊ and for which Lamé's constants are λ∊ and μ. We are interested in the limit behaviour of the inclusion, when ∊ → 0 and μ∊ → ∊; that is when the inclusion becomes thiner and more rigid. Different behaviours are possible, according to the rate at which μ∊ converges to infinity; the limit inclusion may “vanish” if it is not very rigid, but also it may be entirely solid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020302
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  • 12
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    Nonselfadjoint operators in diffraction and scattering (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 327-346 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020307
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  • 13
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    Galerkin's method and stability (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 347-377 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Approximation in least squares by Galerkin's method leads to a consideration of strongly minimal systems. Theorems are derived which permit the recognition of systems which are not strongly minimal from the characteristics of the elements themselves. Normalised systems cannot be strongly minimal without their eigenvalues being bounded above.Speared systems, which have desirable properties, are introduced and their main features determined. Convergence earmarks and error bounds are exposed.A new definition of stability, which is self-checking in a computation, is suggested and its attributes delineated.The extension of the theory to equations involving positive-definite operators is mentioned.
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    URL: http://dx.doi.org/10.1002/mma.1670020308
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  • 14
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    Die Lösung der Prae-Maxwellschen Gleichungen mit Hilfe vollständiger LösungssystemeUnserem verehrten Lehrer, Herrn Prof. Dr. C. Müller, zum 60. Geburtstag gewidmet (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 410-418 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with the Neumann problem of the pre-Maxwell partial differential equations for a vector field v defined in a region G ⊂ R3. We approximate its uniquely determined solution (integrability conditions assumed) uniformly on G by explicitly computable particular integrals and linear combinations of vector fields with a “fundamental” sequence of points .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020404
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  • 15
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    The positivity principle in Boltzmann-type equationsDedicated to Professor Claus Müller on the occasion of his 60th birthday (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 445-456 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Classical theorems about matrices with non-negative elements can be generalized for application in eigenvalue problems of integro-differential form appearing in the description of stationary particle transport. In this way the existence and unicity of positive L1-eigensolutions of the m-quasi-completely-continuous transport operator can be deduced. These solutions can be realized by a method of successive approximation.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670020407
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  • 16
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    A monotonicity property of bessel functionsDedicated to Prof. Dr. C. Müller on the occasion of his 60th birthday (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 480-488 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Some monotonicity results are given for the remainder terms in the asymptotic expansion for x → ∞ of the function Jv(x)Jv+n(x) + Yv(x Yv+n(x), v ε R, n ε Z.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020410
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  • 17
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    Zur Abhängigkeit der Lösung von ut + (h(u))x = 0 von ihren AnfangswertenHerrn Claus Müller zum 60. Geburtstag am 20. 2. 1980 gewidmet (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 504-517 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The above equation has some remarkable properties. In general a global solution exists in a weak sense only, and this solution is not reversible in time. Furthermore it is known, that the solutions for different initial values can coincide for all t ≥ t0 〉 0, and the set of the initial values with this property is convex. Conditions assuring that this set contains only one element are given. This means a weak form of time-reversibility.As a global solution exists only in the weak sense, the classical question concerning dependence of the solution on the initial values needs some modification. This problem is dealt with in suitable L1-norms. It is shown, that the L1-norm of the difference of two weak solutions with respect to the space variable does not increase in time.
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    URL: http://dx.doi.org/10.1002/mma.1670020412
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  • 18
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    Free boundary problems for the laplace equation: A priori estimates, existence theorems, asymptotic behaviours (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 38-69 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work is devoted to Free Boundary Problems with Laplace equation Δu = f in the domain and the two conditions on the Free Boundary u = 1 and |grad u| = λ = const. In the model problems which we study, three cases arise: 1) f = 0, λ is given, 2) f = 0, λ is unknown and the length of the Free Boundary is given, 3) f ≠ 0, λ = 0 (Obstacle Problem).
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670030105
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  • 19
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    A linear Uzawa-algorithm for the steady-state Navier-Stokes problem (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 115-120 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An Uzawa algorithm of Temam is improved so that the Navier-Stokes boundary value problem is reduced to a sequence of linear Poisson problems. A simple finite element method is shown to give a convergent sequence of approximate solutions. Finally a penalty variant is discussed.
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    URL: http://dx.doi.org/10.1002/mma.1670030109
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  • 20
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    On the convexity of equilibrium plasma configurations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 435-443 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the problem of plasma confinement by a magnetic field in an infinite cylinder. We show that if the cylinder has convex cross-section, then there exists an equilibrium plasma configuration with convex cross-section.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030130
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  • 21
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    The impedance boundary value problem for the time harmonic Maxwell equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 475-487 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of a unique solution to Maxwell's equations defined in an exterior domain with impedance boundary condition is established for all frequencies. This is accomplished by reducing this problem to that of solving a system of singular integral equations and then regularizing this system such that the Riesz theory is applicable. We also consider the inverse problem in which it is desired to determine the impedance from a knowledge of the far field pattern. By restricting the impedance to lie a priori in a compact set results are obtained on the existence, uniqueness, and stability of the solution to this inverse scattering problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030133
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  • 22
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    Regularity theorems for Maxwell's equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 523-536 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Methods using the theory of distributions and Hilbert space operators have been very powerful in the past to achieve uniqueness and existence results for Maxwell's equations. In this paper conditions are given when such abstract “Hilbert space”-solutions represent differentiable “regular” functions which satisfy Maxwell's equations, boundary conditions, and transmission conditions in the classical sense.
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    URL: http://dx.doi.org/10.1002/mma.1670030137
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  • 23
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    Masthead (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040101
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  • 24
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    On complete recovery of geophysical data (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 33-73 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: One considers an elastic halfspace with depth (x1) dependent density Q and Lamé moduli (λ,m̈). Impulsive stresses τli = δ(x2, x3)δ(t) for x1 = 0 are applied with displacement responses ui = gi(t, x2, x3) at x1 = 0 (i = 1, 2, 3). Let vi(t, x1) = ∫∫uidx2dx3 (i = 1, 2 is enough) and set w(t, x1) = ∫∫x2u1dx2dx3. One obtains a system of 3 differential equations for v1, v2, and w to which the spectral techniques of inverse scattering theory are applied as in [25]. The inverse problems for the uncoupled vi can then be solved to produce 2 functions A1 and A2 involving (Q, λ, μ) as functions of “bound” variables y1 and y2 containing (Q, λ, μ), between which a relation then is determined. Analysis of the coupled equation for w then leads to a Fredholm integral equation whose solution provides an additional relation between (Q, λ, μ) from which (Q, λ, μ) can be determined as functions of x1. The integral equation is reduced to a Volterra type equation by results and techniques of transmutation and then solved by a modification of standard techniques. A number of features and results of independent mathematical interest arise from the transmutation theory.
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    URL: http://dx.doi.org/10.1002/mma.1670040105
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  • 25
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    Crank-nicolsen-Galerkin approximation for Maxwell's equations (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 123-130 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Maxwell equations are formulated as an evolution equation in a suitable chosen Hilbert space involving a densely defined closed skew-Hermitian operator which generates a unitary group. A Crank-Nicolsen-Galerkin approximation is then established and convergence is shown by arguments from the theory of approximation of groups of operators.
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    URL: http://dx.doi.org/10.1002/mma.1670040109
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  • 26
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    On the transition from supercritical to subcritical Hopf bifurcations (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 143-163 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: By using the method of averaging, we give a complete Hopf bifurcation diagram when the differential equation has more than one parameter. The method is applied to a system of parabolic equations with nonlinear coupling on the boundary. This set of equations is a mathematical model which describes the normalized concentrations of substances in a solution produced by two enzymes.
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    URL: http://dx.doi.org/10.1002/mma.1670040111
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  • 27
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    Bifurcation problems for discrete variational inequalities (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 243-258 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The buckling of a beam or a plate which is subject to obstacles is typical for the variational inequalities that are considered here. Birfurcation is known to occur from the first eigenvalue of the linearized problem. For a discretization the bifurcation point and the bifurcating branches may be obtained by solving a constrained optimization problem. An algorithm is proposed and its convergence is proved. The buckling of a clamped beam subject to point obstacles is considered in the continuous case and some numerical results for this problem are presented.
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    URL: http://dx.doi.org/10.1002/mma.1670040116
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  • 28
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    Finite element approximation of vector fields given by curl and divergence (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 328-335 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a finite element approximation scheme for the system curl is considered. The use of pointwise approximation of the boundary condition leads to a nonconforming method. The error estimate is proved and numerically tested.
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    On the existence of small-amplitude optimum hydrofoil propulsion (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 424-434 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The trust production by means of a periodic heaving motion of a rigid profile is discussed. It is proved by using Bauer's maximum principle, that when a constraint is put on the magnitude of the amplitude, optimum motions do exist.
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    On the Vlasov hierarchy (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 445-455 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Motivated by a recent paper of H. Narnhofer and G. Sewell, we investigate the problem of existence and uniqueness of solutions of the Vlasov hierarchy. It is shown that the unique solution of the Vlasow hierarchy is induced by the flow on the space of probability measures on R6 which is obtained from the solution of the Vlasov equation.
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    Condition number of matrices derived from two classes of integral equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 364-392 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate some integral equations, i. a. the so-called Kupradze functional equations, where the two variables of the kernel belong to two different point sets. An extensive survey of the literature shows the various applications of these equations.By a discretization of the integral equations they are replaced by systems of linear algebraic equations. The condition number of the corresponding matrices is investigated, analytically and numerically. It is thereby quantitatively found in which way the condition of the matrices deteriorates when the two point sets are moved away from each other.
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    Asymptotic analysis of the linear Boltzmann equation (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 405-423 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The stiff boundary value problem for the time-independent linear Boltzmann equation is considered in the variational formulation in terms of the coercive symmetric bilinear form. It is shown that it is asymptotically equivalent to the related variational diffusion problem when the stiffness parameter tends to zero. Higher order perturbations are also discussed.
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    An integral equation approximation of the mixed problem for the laplacian in R3 (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 456-474 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An integral representation for the solutions of the interior and exterior homogeneous mixed problems on a regular bounded open set in R3 is given in terms of a potential of simple layer on the Dirichlet data and of double layer on the Neumann data. A coercive non-symmetric bilinear form is provided. Singular finite elements containing the first terms of the assymptotic expansion of the singularity are built and error estimates for the surface distributions are given.
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    Stability and instability of the energy dependent diffusion system in reactor dynamics (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 488-505 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The purpose of this paper is to give a systematic analysis for the linear energy dependent diffusion system in reactor dynamics, taking into consideration of delayed neutrons. This analysis includes the existence of a unique positive solution for the time dependent system, the asymptotic behaviour of the solution as t → ∞, the stability and instability of steady-state solutions, and the existence and uniqueness of a steady-state solution for the time-independent system. Using the notion of upper and lower solution, we establish some threshold conditions for insuring the asymptotic behaviour of the solution and the stability and the instability of any given unperturbed solution, including steady-state solution. In fact, these conditions characterize the stability and the instability property of the solution, and yield a bifurcation result in terms of either the size of the diffusion domain or the physical parameters of the diffusion medium. We also discuss the case without the effect of delayed neutrons.
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    Einige singuläre Integralgleichungen in der Relaxationsgasdynamik (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 537-550 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The relaxation drag of a slender profile or profile arrangement in plane, steady, relaxing subsonic gas flow is studied. Especially, the question is discussed which shapes the profiles must have in order to minimize the relaxation drag. These optimization problems lead to a number of singular integral equations of first kind, one of which is solved as an example with the help of a suitable chosen ansatz.
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    Solvability of some overdetermined elliptic system in a domain with corners π/n (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 15-18 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In the paper we prove the existence and uniqueness of solutions of the overdetermined elliptic system \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {\left( {\rm A} \right)} & {{\rm rot }\upsilon {\rm = }\omega } & {{\rm div }\upsilon {\rm = 0}} & {\upsilon \cdot {\rm }\bar n|_{\partial \Omega } = b} \\ \end{array} $$\end{document} where b, ω are given functions, in a domain Ω C R3 with corners π/n, n = 2, 3, … The proof is divided on two steps, we construct a solution for the Laplace equation in a dihedral angle π/n, using the method of reflection and we get an estimate in the norms of the Sobolev spaces in some neighbourhood of the edge. In the dihedral angle system (A) reduces to the Dirichlet and Neumann problems for the Laplace equation. In the next step we prove the existence of solutions in the Sobolev spaces Wpl(Ω) using the existence of generalized solutions of (A).
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    Subsonic irrotational flows in multiply connected domains (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 230-242 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solvability of a boundary value problem for a nonlinar elliptic partial differential equation in a plane, bounded, multiply connected domain is investigated. The solution of the problem is equal to unknown constants on inner components of the boundary. We want to determine these constants so that the solution satisfies the so-called trailing conditions. The results have immediate applications in hydrodynamics.
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    A generalized Lane-Emden-Fowler equation (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 259-271 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The nonlinear potential problem Δ φ = -r2m 0, n = m is studied with r ≥ 0, n ε (½, ∞), m ε (-1, ∞) and n m 〉 0.With various additional conditions we have regular and singular solutions which can be studied explicitly by homology transformation. It is proved that if m - n + 1 = 0 the solution with φ(0) = 1, ≠ (0) = 0 is radiusstable. Numerical analysis of a number of cases with m - n + 1 = 0 yields the same conclusion.
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    Galerkin approximations for the equation Lu + Nu = f (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 286-290 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Introducing the concept of a supercontinuous operator, we obtain a general convergence theorem for Galerkin approximations. Under the stronger assumption that N is a monotone operator with N(0) = 0, we show norm convergence of the unique Galerkin approximations to the unique solution.
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    Biorthogonal sequences of solutions of the generalized feller equation (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 317-353 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The generalized Feller equation is a linear, autonomous, parabolic equation of a positive space variable and a time variable. Its coefficients are power functions of the space variable, and they depend on four parameters. In general, the equation is singular at the origin and at infinity. It contains as special cases the special Feller equation, the Kepinski equation, and the standard heat equation. The main objective of the present paper is to establish series expansions of solutions of the generalized Feller equation in terms of the elements of two sequences of particular solutions. The elements of one of these sequences are particular initial condition solutions. The two sequences are biorthogonal. The main result is that a solution does have the desired expansion property if and only if it has the Huygens property in some neighborhood of the origin of the time variable.
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    Ein gemischtes randwertproblem der kreiszylinderschale mit beliebigen ausschnitten (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 354-381 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The problem of stress determination in the area of cut-outs in circular cylindrical shells at given loads is of great interest in industrial practice. This work deals with a mixed boundary value problem of a differential equation derived according to the theory of shallow shells. On part Ct1 of the boundary, the displacements are given, whereas the stresses are specified on the remaining part Ct2. Starting from the Betti-Maxwell principle and with the aid of the fundamental solutions for unit loads and unit displacements, integral representations can be derived for the displacement functions as well as the stress functions.The problem is then transformed into an equivalent system of Fredholm integral equations of the first kind with logarithmic kernels as the main part. As the integral equations together with the auxiliary conditions form a strongly elliptical system of pseudo-differential operators, the Galerkin method converges. Assuming that curves Ct1 and Ct1 do not have points of intersection and that the data are sufficiently regular, the required functions are approximated by cubic splines and, for simplicity's sake, the integral equation system is solved by approximation with a collocation method. In view of the complicated terms of the kernel functions, the kernels are split into a regular and a singular part, the regular part being in turn replaced by cubic splines. The remaining integrations are done numerically by means of Gaussian quadrature formulae. The applicability of the method is demonstrated with the example of a cylinder under internal pressure.
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    Zum 80. Geburtstag von Wolfgang Haack (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 451-453 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Additional Material: 1 Ill.
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    Approximation of the signorini problem with friction, obeying the coulomb law (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 422-437 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: The approximation of the Signorini problem with friction by mixed finite element method is studied. The relation between the continuous case and its finite dimensional discretization is analyzed.
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    Free boundary problem for a two-layer inviscid incompressible fluid (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 476-490 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: The existence of a local (in time) classical solution of a free boundary problem for a two-layer inviscid incompressible fluid is shown. The method of successive approximations and the novel approach to Lagrangian coordinates of Solonnikov are used.
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    Masthead (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Solvability of an initial boundary value problem for the euler equations in twodimensional domain with corners (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 1-22 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The aim of this paper is to prove the existence and uniqueness of local solutions of some initial boundary value problems for the Euler equations of an incompressible fluid in a bounded domain Ω ⊂ R2 with corners. We consider two cases of a nonvanishing normal component of velocity on the boundary. In three-dimensional case such problems have been considered in papers [12], [13], [14]. Similar problems in domains without corners have been considered in [2]-[6], [11]. In this paper the relation between the maximal corner angle of the boundary and the smoothness of the solutions is shown. The paper consists of four sections. In section 1 two initial boundary value problems for the Euler equations are formulated. In section 2 the existence and uniqueness of solutions of the Laplace equation in twodimensional domain with corners for the Dirichlet and Neumann problems is proved in the Sobolev spaces. In sections 3 and 4 we prove the existence and uniqueness of solutions of problems formulated in section 1, using the method of successive approximations.
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    Faedo-galerkin approximations in equations of evolution (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 41-54 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We consider the evolution equation u' = Au + Nu u(0) = φu is a function on a real interval [0, T] with values in a Hilbert space H, A is a linear operator in H generating a continuous semigroup eAt and N is a nonlinear operator in H.We show that 1Existence of the exact solution implies existence of the Faedo-Galerkin Approximations.2Existence of the Faedo-Galerkin Approximations implies existence of the exact solution.3Uniform convergence of the Faedo-Galerkin Approximations to the exact solution.The Paper consists of two parts. In the first five sections we require that A possesses a complete orthonormal system of eigenfunctions, in section 6 we drop this requirement.
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    Functional differential equations with certain monotonicity properties (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 97-103 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The present paper is concerned with the study of retarded differential equations in n-space, which satisfy some monotonicity properties. Sufficient conditions are given guaranteeing that solutions are contained in the probability (n - 1)-simplex. Existence and uniqueness of constant solutions are proved. It is also shown that every solution converges to a constant as t → ∞.
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    Asymptotic behavior of a nonhomogeneous predator-prey system with one diffusing and one sedentary species (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 40-67 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In general the predator-prey system studied will have many equilibrium states with different “patches”, i.e. regions where the sedentary species vanishes. If one equilibrium is given, a Ljapunov functional can be constructed for a set of initial data with patches satisfying a certain compatibility condition. By the methods of Alikakos [1] and Rothe [28] this implies uniform bounds for the diffusing species in a Hölder space and the sedentary species in a Lp-space. Considering pieces of the trajectory for time in some bounded interval and using the weak*-topology for the sedentary species, one defines an ω-limit set which is compact and nonvoid. Using the Ljapunov functional an asymptotic version of the differential equations is derived. It turns out that they admit only constant solutions except for a very special case. Thus convergence to the equilibrium follows.
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    A trace theorem for solutions of the wave equation, and the remote determination of acoustic sources (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 131-152 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The determination of sources of acoustic wave motion in several dimensions from remote measurements is of considerable interest in many applications, and the underlying mathematical problem is quite ill-posed. We separate the source determination problem into a control problem for the wave equation and an inverse mixed initial-boundary value problem, and concentrate on the latter, in which the initial data for a solution of the wave equation are to be determined from its trace on a time-like hyperplane. Though the geometry of this problem is simple, it exhibits some of the central analytic difficulties of more complex problems. We prove a uniqueness theorem, give examples of instability, establish regularity properties of the trace, and locate noncompact classes of stable functionals. The existence of these noncompact classes shows that the problem is “partially well-posed”, i.e. that smoothing in all directions is not required to regularize the problem, and distinguishes it from most other ill-posed problems, such as backwards diffusion and analytic continuation.
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    Asymptotic equipartition of energy for equations of elasticity (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 186-194 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we give a review of the equipartition of energy results of Goldstein and Sandefur [3], [4], [5] as well as proving a new result in the case of a particular fourth order equation. These results are then applied to the equations of elasticity to give a weak asymptotic orthogonality for the shear and pressure waves. In the case of boundary value problems in the interior of a bounded domain we get weak asymptotic orthogonality in the average.
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    Bifurcation of periodic orbits in coupled chemical reactors II (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 216-232 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: In this part of the paper we deal with computational aspects of the bifurcation problem introduced in Part I, cf. [1]. It follows from Section 3 that the bifurcation behaviour is essentially determined by the expression KP(Ω) - ∧β, where β is some constant which was assumed to be nonzero, while P(Ω) is some 2π-periodic function which was implicitly defined in Section 2. In Section 4 we first derive easily computable expressions for P(Ω) and β from the definitions of Section 2. Secondly we offer a direct, although formal, derivation for these quantities. In Section 5 we briefly show how P(Ω). β can actually be computed by means of a high speed computer and discuss a number of examples. In Section 6 finally we give some asymptotic results for systems depending on an additional parameter.
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    Interactions of fast and slow waves in hyperbolic systems with two time scales (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 292-307 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider certain symmetric hyperbolic systems of nonlinear partial differential equations whose solutions vary on two time scales. The large part of the spatial operator is assumed to have constant coefficients, but a nonlinear term multiplying the time derivatives is allowed. We show that if the initial data are not prepared correctly for the suppression of the fast scale motion, but contain errors of amplitude O(∊), then the perturbation in the solution will also be of amplitude O(∊). Further, if the large part of the spatial operator is nonsingular, we show that the error introduced in the slow scale motion will be of amplitude O(∊2), even though fast scale waves of amplitude O(∊) will be present in the solution.
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    Transmutation via the momentum plane (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 467-495 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Transmutation methods are developed for equations of the form x2 ϕ“ + x2(k2” - q̃(x)) ϕ = (v2 - (1/4)) ϕ, with v as spectral variable, which correspond to problems in quantum scattering theory at fixed energy k2 (here v ˜ l + (1/2) with l complex angular momentum). Spectral formulas for transmutation kernels are constructed and the machinery of transmutation theory developed by the author for spectral variable k is shown to have a version here. General Kontrorovič-Lebedev theorems are also proved.
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    Two remarks on continuation procedures for solving some nonlinear equations (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 512-514 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let F be a mapping from Rn+1 into Rn, x(t) be a parametrization for ∣t - t0 ∣ 〈 c, of a smooth solution branch of the equation F(x) = 0, A(t) be the jacobian (n + 1) associated to a standard continuation method used for computing the solution branch. We study for a class of singularities at x(t0) the behaviour, near t = t0, of the determinant of A(t).
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    URL: http://dx.doi.org/10.1002/mma.1670060131
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    On the Vlasov-Fokker-Planck equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 527-538 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a modification of the Vlasov-Poisson equation, obtained by adding a diffusion term with respect to velocity. It describes, from a physical point of view, a plasma in thermal equilibrium, in a mean field limit situation. We find that the already known results concerning existence and uniqueness of the solutions for the ordinary Vlasov equation (constructive results and counterexamples) translate to our case.
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    URL: http://dx.doi.org/10.1002/mma.1670060134
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    Scattering theory for diffraction gratings (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 158-158 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060111
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    Évolution quasi-statique des milieux visco-plastiques de maxwell-norton (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 192-205 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we deal with the existence and unicity of a solution of the Maxwell-Norton quasi-static problem. Some fundamental results concerning the functional spaces are first recalled. Then, by an implicit scheme, we obtain a discretized problem which is well-posed. By monotonicity techniques, we finally prove the convergence of the discrete solutions to the solution of the initial problem.
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    URL: http://dx.doi.org/10.1002/mma.1670060113
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    L2-boundary integral equations for the robin problem (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 345-352 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study an integral equation method for the exterior Robin problem for the Helmholtz equation where the boundary condition is interpreted in the L2-sense. In particular, we derive a composite integral equation from Green's theorem which is uniquely solvable for all wave numbers.
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    URL: http://dx.doi.org/10.1002/mma.1670060121
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    Some applications of a galerkin-collocation method for boundary integral equations of the first kind (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 280-325 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Here we apply the boundary integral method to several plane interior and exterior boundary value problems from conformal mapping, elasticity and fluid dynamics. These are reduced to equivalent boundary integral equations on the boundary curve which are Fredholm integral equations of the first kind having kernels with logarithmic singularities and defining strongly elliptic pseudodifferential operators of order - 1 which provide certain coercivity properties. The boundary integral equations are approximated by Galerkin's method using B-splines on the boundary curve in connection with an appropriate numerical quadrature, which yields a modified collocation scheme. We present a complete asymptotic error analysis for the fully discretized numerical equations which is based on superapproximation results for Galerkin's method, on consistency estimates and stability properties in connection with the illposedness of the first kind equations in L2. We also present computational results of several numerical experiments revealing accuracy, efficiency and an amazing asymptotical agreement of the numerical with the theoretical errors. The method is used for computations of conformal mappings, exterior Stokes flows and slow viscous flows past elliptic obstacles.
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    Exact and chapman-enskog solutions for the carleman model (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 417-432 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Chapman-Enskog procedure is applied to the Carleman model of the Boltzmann equation. It has been proved that the Carleman equations possess a solution on the time interval on which a smooth solution of the fluid-like equation exists. The calculations have been performed up to the first order i.e., to the Navier-Stokes-like equation. It has been shown that in this case a difference between an exact solution and the Chapman-Enskog solution is of order ∊2. Extension of the results to higher orders is also possible. This gives a justification of the Chapman-Enskog procedure as an asymptotic expansion method.
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    On the geometric form of free boundaries satisfying a bernoulli condition (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 449-456 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: In the x-y plane, let Ω denote an annular domain bounded by the simple closed curves ⌜ and ⌜*, such that the capacity potential U in Ω satisfies ∣ ▽ U∣ = 1 on ⌜. Assuming ⌜* to be known, we obtain qualitative properties of ⌜. For example, the number of local maxima or minima of the y-co-ordinate relative to ⌜ cannot exceed the corresponding number for ⌜*.
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    URL: http://dx.doi.org/10.1002/mma.1670060127
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    Masthead (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670020101
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    Convergence of semigroups with an application to the carleman equationWork performed under the auspices of the U.S. Department of Energy. (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 303-308 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a simple proof of a convergence result for nonlinear semigroups which can be applied to obtain the fluid dynamical limit of Carleman's equation. In addition, we explicitly identify a closed exponential generator of the limit semigroup. Our results are closely related to those of T. G. Kurtz and H. P. McKean.
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    Discontinuous self-excited systems: An asymptotic analysis (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 309-326 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we derive a uniformly valid asymptotic approximation of the periodic solution of a self-excited system given by the differential equation and β1,β2, are positive constants. By uniformly valid asymptotic approximation we mean that no secular terms are present. Our procedure makes use of a nonlinear change of independent variable that transforms the problem from one in which the discontinuities are ∊ dependent to one in which the discontinuities are ∊ independent. We obtain an asymptotic approximation up to order ∊ of the periodic solution and an asymptotic approximation up to order ∊2 of the period. Some comparisons between our asymptotic results and numerically derived results are given. Application of our technique to other examples of self-excited systems is discussed. The equation is investigated in detail.
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    Außenraumaufgaben in der linearen ElastizitätstheorieDiese Arbeit entstand mit Unterstützung des durch die Deutsche Forschungsgemeinschaft getragenen Sonderforschungsbereiches 72 an der Universität Bonn.Herrn Claus Müller zum 60. Geburtstag am 20. 2. 1980 gewidmet (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 379-396 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper starts with a short survey of the treatment of initial-boundary-value problems in temperature-free linear elasticity with unisotropic media. The main part of the paper is concerned with exterior initial-boundary-value problems in thermoelasticity. In this case the underlying differential operator A is no longer selfadjoint. Thus the spectrum of A has to be discussed. In 2.1 it is shown that all λ with Re λ 〈 0 belong to the resolvent set. In 2.2 the case G = R3 with homogeneous isotropic media is considered. Let Λ be the essential spectrum in this case. In 2.3 Λ depending on the thermic coupling parameter is discussed. 2.4 treats the spectrum of A assuming the medium to be homogeneous and isotrop outside a large ball. In this case Λ is the essential spectrum for A too. Radiation conditions are formulated. Finally 2.5 presents a short treatment of the time dependent case with Laplace-transformation.
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    Ein Existenzsatz für die Vlasov-Gleichung mit selbstkonsistentem MagnetfeldProf. Dr. C. Müller gewidmet anläßlich seines 60. Geburtstages - in Dankbarkeit für viele Anregungen, auch zu der hier behandelten Problemstellung. (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 429-444 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The Vlasov equation with electric and magnetic fields generated by the distribution of the plasma is considered. For a simplified model with one space and two velocity coordinates and a mollification of the spatial density and the mean velocity in the Maxwell equations an existence and uniqueness theorem is proved.
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    Monoton einschließend konvergente iterationsprozesse vom gauß-seidel-typ zur lösung nichtlinearer gleichungssysteme im RN und anwendungenHerrn Professor Dr. Claus Müller zum 60. Geburtstag gewidmet (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 489-503 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: In this paper we describe a class of Gauß-Seidel iterations for the solution of large sparse nonlinear systems of equations. For suitable starting vectors every method of this class is monotonically convergent with respect to both sides. The result will be applied to the numerical solution of nonlinear boundary-value problems and boundary layer problems.
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    Masthead (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    On the boundary value problem of the biharmonic operator on domains with angular corners (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 556-581 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper is concerned with boundary singularities of weak solutions of boundary value problems governed by the biharmonic operator. The presence of angular corner points or points at which the type of boundary condition changes in general causes local singularities in the solution. For that case the general theory of V. A. Kondrat'ev provides a priori estimates in weighted Sobolev norms and asymptotic singular representations for the solution which essentially depend on the zeros of certain transcendental functions. The distribution of these zeros will be analysed in detail for the biharmonic operator under several boundary conditions. This leads to sharp a priori estimates in weighted Sobolev norms where the weight function is characterized by the inner angle of the boundary corner. Such estimates for “negative” Sobolev norms are used to analyse also weakly nonlinear perturbations of the biharmonic operator as, for instance, the von Kármán model in plate bending theory and the stream function formulation of the steady state Navier-Stokes problem. It turns out that here the structure of the corner singularities is essentially the same as in the corresponding linear problem.
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    Bifurcation results for a class of periodic quasi-linear parabolic equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 11-20 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the problem where a and f are 1-periodic in t, a is positive, f satisfies appropriate decreasing conditions; smoothness of a, f, ∂Ω is also assumed. Denote by λ0 the principal eigenvalue of Δ with zero Dirichlet boundary conditions, and define . We prove: (a) if ε ≤ 0, then no non-negative periodic solution exists but zero, and any solution with continuous non-negative initial datum converges to zero uniformly as t → ∞; (b) if ε 〉 0, then a unique non trivial non-negative 1-periodic solution u* exists, and any solution with continuous, non-negative not identically zero initial datum approaches uniformly u* as t → ∞.
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    Irregular multipoint eigenvalue problems (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 88-103 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove asymptotic estimates for the Green's function of irregular multipoint eigenvalue problems, these estimates are fundamental for the expansion of functions into a series of eigenfunctions of irregular eigenvalue problems.
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    The decay of solutions of the Carleman model (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 121-127 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove that for positive initial data u0, v0 ∊ C1 (R) ∩ L1 (R) vanishing at infinity, the solution u(x, t) v(x, t) of the Carleman model satisfies the estimate The constant C depends only on the initial mass m.
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    New asymptotic expansion algorithm for singularly perturbed evolution equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 172-188 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new asymptotic expansion algorithm related to the Chapman-Enskog expansion in kinetic theory is applied to systems of linear evolution equations. The uniform convergence of the asymptotic solution to the exact one is shown. The algorithm is applied to the linearized Carleman model of the Boltzmann equation, to the neutron transport equation, and to the Fokker-Planck equation.
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    Randwertaufgaben in der verallgemeinerten Potentialtheorie (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 218-228 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Neumann and Dirichlet boundary value problem of generalized potential theory is considered. Based on a compact imbedding result, existence and uniqueness theorems are obtained for Riemannian manifolds with compact boundary (‘interior and exterior domains’).
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    A singular perturbation problem for linear operators with an application to electrostatic and magnetostatic boundary and transmission problemsPart of this work was carried out while both authors were at the Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA. (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 249-274 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The treatment of certain electro- and magnetostatic boundary and transmission problems by boundary integral equations leads to parameter-dependent integral equations of the second kind. The integral operators involved have the property that the dimension of their nullspaces changes between two nonzero values (depending on the geometry of the problem) as the parameter tends to zero. We investigate the continuous dependence of solutions to these equations on the parameter. To this end, we treat the problem of continuous dependence of solutions to parameter-dependent linear operator equations of the second kind in a Banach space in the framework of generalized inverses.
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    URL: http://dx.doi.org/10.1002/mma.1670030118
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    Über das asymptotische Verhalten thermoelastischer Wellen im R3Diese Arbeit entstand mit Unterstützung des durch die Deutsche Forschungsgemeinschaft getragenen Sonderforschungsbereiches 72 an der Universität Bonn. (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 312-317 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In [L] the author provided existence theorems for initial-boundary-value problems in thermoelasticity for unbounded domains. Continuing this work the asymptotic behaviour of solutions in R3 with respect to t → ∞ will be described in this paper.
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    URL: http://dx.doi.org/10.1002/mma.1670030122
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    High Hartmann number flow through a rectangular duct with unequally and finitely conducting walls (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 531-544 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Nonsymmetric Hartmann flow through a rectangular duct is investigated for thin duct walls with, generally, unequal but finite conductivities. A high Hartmann number is adopted. Consistent with known phenomena, both Hartmann layers transverse to the applied magnetic field are assumed to be separated from the two side boundary layers by four corner regions plus four inner corner regions. The method of singular perturbations and matched asymptotic expansions is applied to the coupled system. The equations governing the core and Hartmann layers are first partially resolved for leading terms. This is then followed by tackling equations governing one side layer and two adjacent corner regions. The latters' incorporation secures, for the former, only those boundary conditions that are compatible along the transverse walls. Both corner regions are denied access to non-required boundary conditions along the neighbouring side wall by the adjoining inner corner regions. However, the latters' boundary value problems need not be tackled for the acquirement of only dominant terms beyond all four inner corner regions. The complementary side layer and associated corners are accounted for by a non-symmetric reflection principle.Results reveal that a difference between conductivities in the transverse walls together with at least one finitely conducting side wall impart to disturbances within the core and Hartmann layers (i) a nontrivial dependence on the transverse coordinate relative to the magnetic field and flow in addition to the (usual) dependence on the field aligned coordinate,(ii) a dependence on side wall parameters in addition to the dependence on transverse wall parameters.Applications to related situations are considered. These include the case for a perfectly conducting lower wall, a finitely conducting upper wall, and equally and finitely conducting side walls.
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    Asymptotic relationship between telegraphic and diffusion equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 21-37 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the paper it is considered the generalized telegraphic equation represented by the system of four evolution equations, containing a small positive parameter multiplying some of the time derivatives. It is shown that if the small parameter tends to zero, the solution to the telegraphic equation tends asymptotically to the solution of the diffusion equation obtained from the former one by putting the small parameter equal to zero.
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    Sur une Interprétation Mathématique de l'Intégrale de Rice en Théorie de la Rupture Fragile (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 70-87 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We formulate the assumptions under which Rice J integral and the critical energy release rate, which occur in fragile fracture mechanic, are equivalent.
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    A constructive approximation theorem for the oblique derivative problem in potential theory (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 104-114 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The (exterior) oblique derivative problem of potential theory is considered where l is a C(1,λ)-vector field on a regular boundary ∂Ge in Euclidean space R3 and the direction l at any point of ∂Ge forms with the outside normal n an angle ∢ (l, n) satisfying cos ∢ (l, n) ≥ c 〉 0. An approximation of the uniquely determined solution is given by use of trial functions {Φn}n=0,1,… harmonic in some region containing Ge and suitable for numerical purpose (for instance: solid spherical harmonics, certain sequences of fundamental solutions). The system {l▽Φn+hΦn}n=0,1,… defined on ∂Ge is shown to be closed and complete in the pre-Hilbert space C(0,λ)(∂Ge) of λ-Hölder continuous functions.
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    URL: http://dx.doi.org/10.1002/mma.1670030108
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    Scattering techniques for a one dimensional inverse problem in geophysics (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 145-171 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A one dimensional problem for SH waves in an elastic medium is treated which can be written as vtt = A-1 (Avy)y, A = (ϱμ)1/2, ϱ = density, and μ = shear modulus. Assume A ∊ C1 and A′/A ∊ L1; from an input vy(t, 0) = ∂(t) let the response v(t, 0) = g(t) be measured (v(t, y) = 0 for t 〈 0). Inverse scattering techniques are generalized to recover A(y) for y 〉 0 in terms of the solution K of a Gelfand-Levitan type equation, .
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    URL: http://dx.doi.org/10.1002/mma.1670030112
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    A model equation for Non-Newtonian fluids (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 200-217 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A one-dimensional model for the equations of motion of a “simple fluid” according to Noll is proposed. An exterior problem for the model equation is solved by means of a transform method.
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    URL: http://dx.doi.org/10.1002/mma.1670030115
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    Necessary and sufficient conditions for the existence of shock curves of hyperbolic 1-conservation laws (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 275-286 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present three conditions for the existence of shock curves of hyperbolic 1-conservation laws. If at least two of the conditions hold, then shock curves exist uniquely in the classical sense. We present an example (Example 2, Section 4) for which two of the conditions do not hold and a new kind of singularity occurs. In Remark 1 we present two other conditions similar to the above three conditions which also imply the existence of shock curves.
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    URL: http://dx.doi.org/10.1002/mma.1670030119
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    Bifurcation of periodic orbits in coupled chemical reactors I (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 301-311 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper provides a rigorous approach to the problem of bifurcation of periodic orbits of a chemical reactor system recently studied by Marek and Stuckl, and by Neu. Using transformation techniques and invariant manifold theory the problem is reduced to a two-parameter bifurcation equation in R.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670030121
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    Monotone schemes for semilinear elliptic systems related to ecology (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 272-285 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Semilinear elliptic systems of partial differential equations related to ecology are studied, with Dirichlet boundary conditions. Monotone sequences of functions which satisfy scalar equations are constructed so that they will converge to upper and lower bounds for the solutions of the systems. In case a related system has a unique positive solution, then these sequences will converge to the solution of the original system. Applications of the monotone sequences to uniqueness and stability are also given.
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    URL: http://dx.doi.org/10.1002/mma.1670040118
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    Spectral properties of certain stiff problems in elasticity and acoustics (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 291-306 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider two vibration problems containing a small parameter → 0: a) Vibration of an elastic, slightly compressible body, and b) acoustic vibration of a slightly viscous compressible barotropic fluid in a vessel.The asymptotics of eigenvalues for problem a) is studied by using a uniformly convergent expansion of the stiff type. After a re-scaling of the spectral parameter, the problem b) reduces to an analogous problem, and we prove that, as ε → 0, infinitely many eigenvalues converge to 0 (which is an eigenvalue of infinite multiplicity of the corresponding inviscid acoustic problem).
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    URL: http://dx.doi.org/10.1002/mma.1670040120
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    Spline methods in geodetic approximation problems (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 382-396 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with spline methods in a reproducing kernel Hilbert space consisting of functions defined and harmonic in the outer space of a regular surface (e.g. sphere, ellipsoid, telluroid, geoid, (regularized) earth's surface). Spline methods are used to solve interpolation and smoothing problems with respect to a (fundamental) system of linear functional giving information about earth's gravity field. Best approximations to linear functionals are discussed. The spline of interpolation is characterized as the spline of best approximation in the sense of an appropriate (energy) norm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040124
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    A minimax principle for nonlinear eigenvalue problems with applications to nonoverdamped systems (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 415-424 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The theory of Rayleigh functionals for non-linear eigenvalue problems T(λ) u = 0 is extended to cases where the functional is defined only on a proper subset. The theory applies to problems which do not satisfy an overdamping condition and yields a minimax characterization of eigenvalues. Applications to damped free vibrations of an elastic body are discussed.
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    URL: http://dx.doi.org/10.1002/mma.1670040126
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    On spherical spline interpolation and approximation (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 551-575 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Spherical spline functions are introduced by use of Green's surface functions with respect to the (Laplace-)Beltrami operator of the (unit) sphere. Natural (spherical) spline functions are used to interpolate data discretely given on the sphere. A method is presented that allows the smoothing of irregularities in measured values or experimental data. Extensions of Peano's theorem and Sard's theory of best approximation to the spherical case are given by integral formulas. Schoenberg's theorem is transcribed into spherical nomenclature.
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    URL: http://dx.doi.org/10.1002/mma.1670030139
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    Local solvability of a nonstationary leakage problem for an ideal incompressible fluid, 3 (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 1-14 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove the existence and uniqueness of solutions of the leakage problem for the Euler equations in bounded domain Ω C R3 with corners π/n, n = 2, 3… We consider the case where the tangent components of the vorticity vector are given on the part S1 of the boundary where the fluid enters the domain. We prove the existence of an unique solution in the Sobolev space Wpl(Ω), for arbitrary natural l and p 〉 1. The proof is divided on three parts: (1) the existence of solutions of the elliptic problem in the domain with corners \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm rot }\upsilon {\rm = }\omega {\rm, div }\upsilon = 0,\upsilon \cdot \bar n||_{\partial \Omega } = 6 $$\end{document} where v - velocity vector, ω - vorticity vector and n is an unit outward vector normal to the boundary,(2) the existence of solutions of the following evolution problem for given velocity vector \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{l} \omega _t + \upsilon ^\kappa \omega _x \kappa - \omega ^\kappa \upsilon _x \kappa = F \equiv {\rm rot }f \\ \omega |_{t = 0} = \omega _0,\omega |_{s1} = \eta \\ \end{array} $$\end{document}(3) the method of successive approximations, using solvability of problems (1) and (2).
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    URL: http://dx.doi.org/10.1002/mma.1670040102
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    The sommerfeld half-plane problem revisited I: The solution of a pair of coupled Wiener-Hopf integral equationsPresented at a Conference in Diffraction and Scattering Theory held at the Technische Hochschule Darmstadt on May 29, 1980. (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 74-90 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A study and the solution of an extension of the classical Sommerfeld half-plane problem which leads to a pair of integral equations of the Wiener-Hopf type is given. The method of solution is function theoretic in character and employs a combination of the ideas of Wiener and Hopf and Carleman.
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    URL: http://dx.doi.org/10.1002/mma.1670040106
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    A discontinuous nonlinear eigenvalue/Free boundary problem (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 131-142 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the problem \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} { - \Delta u = \lambda H({\rm u - 1)}} & {{\rm in }\Omega } \\ {u = g} & {{\rm in }\partial \Omega } \\ \end{array} $$\end{document}(H is the Heaviside unit step function) in spherical domains Ω of arbitrary dimension. When g = 0, there are two branches of radial solutions; for small nonzero g there are solutions near the corresponding radial solution. Moreover, the set where μ = 1 is in all cases an analytic hypersurface.
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    URL: http://dx.doi.org/10.1002/mma.1670040110
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    On the classical solutions of the initial value problem for the unmodified non-linear vlasov equation II special cases (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 19-32 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The theory of part I is applied to prove several existence and non-existence results for special cases. If N = 3, a global classical solution of P° exists, if ϕ ≥ 0 has rotational symmetry. If N ≥ 4, global classical solutions of P° do not always exist.
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    URL: http://dx.doi.org/10.1002/mma.1670040104
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    On finite element methods for convection dominated phenomena (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 98-122 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The aim of this work is to give theoretical justification of several types of finite element approximations to the initial-boundary value problems of first order linear hyperbolic equations. Our approximate scheme is obtained by the piecewise linear continuous finite element method for space variable, x, and the Euler type step by step integration method for time variable, t. An artificial viscosity technique, up-stream type methods are considered within the frame work of L2-theory. The convergence and the error estimate of the approximate solutions to the true one are discussed.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670040108
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    On the decay of symmetric dynamo fieldsThis work was performed under the terms of the agreement on association between the Max-Planck-Institut for Plasmaphysik and EURATOM. (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 91-97 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The ‘anti-dynamo’ theorems for poloidal magnetic fields with axisymmetry and plane symmetry are generalized to the case of a compressible and time-dependent flow in a fluid with arbitrary conductivity.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670040107
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    Boundary integral equations for the Helmholtz equation: The third boundary value problem (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 164-193 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study the application of boundary integral equation methods for the solution of the third, or Robin, boundary value problem for the exterior Helmholtz equation. In contrast to earlier work, the boundary value problem is interpreted here in a weak sense which allows data to be specified in L∞ (∂D), ∂D being the boundary of the exterior domain which we assume to be Lyapunov of index 1. For this exterior boundary value problem, we employ Green's theorem to derive a pair of boundary integral equations which have a unique simultaneous solution. We then show that this solution yields a solution of the original exterior boundary value problem.
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    URL: http://dx.doi.org/10.1002/mma.1670040112
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    Das asymptotische verhalten der greenschen funktion N-irregulaärer eigenwertprobleme mit zerfallenden randbedingungen (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 331-345 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove asymptotic estimates for the Green's function of N-irregular eigenvalue problems My = λNγ with splitting boundary conditions.In contrast to the N-regular case the Green's function G(x,ζ,λ) grows exponentially for |λ| → ∞ if x 〉 ζ.These estimates are fundamental for the expansion of functions into a series of eigenfunctions of N-irregular eigenvalue problems. In a subsequent paper it will be shown that this irregular behavior of G(x,ζ,λ) implies that only a very small class of functions can be expanded into a series of eigenfunctions of such problems.
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    URL: http://dx.doi.org/10.1002/mma.1670050122
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    On the convergence of the multigroup approximations for submultiplying slab media (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 206-229 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The stability, convergence, and consistency properties of the steady-state multigroup model are investigated for submultiplying slab media. These concepts are defined in a Banach space setting in which the norm of the angular flux is the collision density integrated over phase space. It is shown that the multigroup approximations are stable and are both consistent with, and convergent to, the transport equation under the conditions that the maximum fluctuations in the total cross section and in the expected number of secondary particles, arising from each energy level, tend to zero as the energy mesh becomes finer. A concluding discussion deals with pathologies of the multigroup approximation for situations in which these fluctuations do not tend to zero as the norms of the energy partitions. The results in this paper complement the time-dependent results of Belleni-Morante and Busoni for isotropic slabs and the results of Nelson for steady-state rod media.
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    URL: http://dx.doi.org/10.1002/mma.1670040114
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    Existence and uniqueness for an equation of mixed type in a rectangle (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 307-316 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A boundary value problem is considered for an equation of mixed type in a rectangle. An energy method is used to prove uniqueness for appropriate boundary conditions. Similar considerations for the adjoint problem allow one to prove the existence of a generalized solution to the problem. It is also shown that the energy method leads naturally to a finite element method. The method is described for a special case and convergence is shown for the resulting numerical procedure.
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    URL: http://dx.doi.org/10.1002/mma.1670040121
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