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  • Articles  (39)
  • Mathematics and Statistics
  • Wiley-Blackwell  (39)
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  • 2005-2009
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  • 1980-1984  (39)
  • 1981  (39)
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  • Articles  (39)
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  • Wiley-Blackwell  (39)
  • American Institute of Physics (AIP)
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  • 2005-2009
  • 1990-1994
  • 1980-1984  (39)
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  • 1
    Electronic Resource
    Electronic Resource
    Partial asymptotic stability via limiting equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 516-522 
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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 the limiting equations approach is applied to study the stability properties with respect to a part of the state variables for nonautonomous dynamical systems. Sufficient conditions are given for uniform asymptotic eventual strongly partial stability and for uniform asymptotic partial stability. An application of the results is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030136
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  • 2
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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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030139
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  • 3
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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 
    Details
    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 → ∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030103
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  • 4
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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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  • 5
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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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030109
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  • 6
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    Eine Integralgleichungsmethode für akustische Reflexionsprobleme an lokal gestörten Ebenen (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 128-144 
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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 consider the reflection of acoustic waves at an unbounded surface which coincides with a plane outside a sufficiently large sphere. We prove uniqueness and existence theorems for the corresponding boundary value problems for the reduced wave equation with Dirichlet and Neumann data by employing integral equation methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030111
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  • 7
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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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030118
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  • 8
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030122
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  • 9
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    Stable solutions of some ill-posed problems (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 336-363 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Stable solutions of equations of the first kind and equations of the second kind at a characteristic value are given. Iterative processes for solutions are constructed. Extension of operators is used to turn an ill-posed problem into a well-posed one.
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    URL: http://dx.doi.org/10.1002/mma.1670030125
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  • 10
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    Mathematische Behandlung ernes Modells der Haemodialyse (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 393-404 
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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 simple mathematical model for the process of hemodialysis is presented. This model is based on a system of two linear differential equations of first order with partly discontinuous coefficients that describe the time-development of the concentrations of a certain toxin (like urea) in the intra- and extracellular part of the human body. The main result is the existence of periodic positive solutions of this system under the natural assumption that the generation of the toxin and its removal by hemodialysis are periodic processes. These periodic positive solutions are also computed numerically for a realistic choice of the coefficients of the modelling differential equations.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670030127
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  • 11
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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 
    Details
    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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  • 12
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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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  • 13
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    Study of motions of a vibrating string subject to solid friction (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 287-300 
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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 consider a string moving in its plane and subject to solid friction (Coulomb's law). It is known that when the time increases indefinitely the string reaches an equilibrium position and by analogy with the case of a mass point we ask if the equilibrium is reached after a finite time. We prove that this is the case when the string is initially at rest and 1. when the initial shape possesses a second derivative bounded by certain limits, or 2. when the initial shape is formed by two straight line segments. In the last section we obtain some partial results when the string is initially at rest in the shape of a polygonal line. The case of an arbitrary initial position is still an open problem.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670030120
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  • 14
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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 
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    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, .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030112
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  • 15
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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 
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    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030115
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  • 16
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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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030101
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  • 17
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    Ghosts in tomography - the null space of the radon transform (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 1-10 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let ω0, …, ωp-1 ∊ S1 be p distinct directions and let R denote the Radon transform. The functions f with support in the unit disc and with Rf(s, ωj) = 0 for s ∊ [-1, 1] and j = 0, …, p - 1 are given. „Ghosts“ are constructed, i.e. functions in the null space that pretend not existent tumors. Methods to avaoid such ghosts are indicated.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670030102
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  • 18
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030107
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  • 19
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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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    ISSN: 0170-4214
    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.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670030110
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  • 20
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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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    ISSN: 0170-4214
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030113
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  • 21
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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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    URL: http://dx.doi.org/10.1002/mma.1670030116
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  • 22
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    On the construction of minimizing sequences for convex functionals with upper and lower bounding functionals (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 189-199 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A method is described for constructing upper and lower bounds for the stationary values of a general class of convex functionals. The method relies of the existence of approximating convex functionals whose Gâteaux derivatives are presumed to have simpler structure than the original. The method is iterative in that convergent sequences of bounds can be constructed. Some applications to the Laplacian operator are included.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670030114
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  • 23
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    On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation I general theory (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 229-248 
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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 existence and uniqueness of classical solutions of the initial value problem for Vlasov's equation with an unmodified Newtonian or Coulomb force. We give a necessary and sufficient condition for the existence of a solution on an interval I.
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    URL: http://dx.doi.org/10.1002/mma.1670030117
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  • 24
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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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  • 25
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    Local energy decay of solutions of linearized shallow-water equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 318-327 
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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 the local decay of the energy of the solution to a mixed initial boundary value problem for the linearized shallow-water equations with constant coefficients, where the domain is a half-plane, a certain dissipative boundary condition is prescribed and the initial data have compact support contained in the open half-plane.
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    URL: http://dx.doi.org/10.1002/mma.1670030123
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  • 26
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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.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670030126
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  • 27
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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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    URL: http://dx.doi.org/10.1002/mma.1670030128
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  • 28
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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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    URL: http://dx.doi.org/10.1002/mma.1670030132
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  • 29
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030134
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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 
    Details
    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.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030138
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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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030104
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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 
    Details
    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.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030106
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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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030108
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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.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030121
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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 
    Details
    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.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030124
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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 
    Details
    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.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030129
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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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030131
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    Approximation of the scattering state by means of the radiation boundary condition (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 506-515 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The approximation sequence for the scattering state is constructed by the solutions for the reduced wave equations in some bounded domains with radiation conditions at their boundary. The corresponding discrete approximation is also considered by the Bubnov-Galerkin method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030135
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