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  • Mathematics and Statistics  (705)
  • Wiley-Blackwell  (705)
  • Annual Reviews
  • 2005-2009
  • 1990-1994  (520)
  • 1980-1984  (185)
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  • Wiley-Blackwell  (705)
  • Annual Reviews
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  • 1
    Electronic Resource
    Electronic Resource
    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 
    Details
    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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  • 2
    Electronic Resource
    Electronic Resource
    Nonselfadjoint operators in diffraction and scattering (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 327-346 
    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.1670020307
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  • 3
    Electronic Resource
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    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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  • 4
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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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  • 5
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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).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040102
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  • 6
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    Some decomposition theorems and their application to non-linear potential theory and Hodge theory (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 35-52 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers Dirichlet (or Neumann type) boundary value problems of generalized potential theory \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm d}\alpha = f,\;\delta \varepsilon \left(\alpha \right) = g\,{\rm in}\,M, $$\end{document} \documentclass{article}\pagestyle{empty}\begin{document}$$ \alpha = 0\,{\rm on}\,\partial M $$\end{document} on Lipschitz manifolds with boundary. Here ∊ denotes a permissible non-linearity. The existence theory is developed in the framework of monotone operators. The approach covers a variety of applications including fluid dynamics and electro- and magneto-statics. Only fairly weak regularity assumptions are required (e.g. Lipschitz boundary, L∞-coefficients). As a by-product we obtain a non-linear Hodge theorem generalizing a result by L. M. Sibner and R. J. Sibner (‘A non-linear Hodge-DeRham theorem’, Acta Math., 125, 57-73 (1970)).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670120103
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  • 7
    Electronic Resource
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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 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040119
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  • 8
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040122
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  • 9
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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 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040123
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  • 10
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040129
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  • 11
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    Zur theorie rotierender und schwingender schaufelkränze in einer unterschallstromung durch einen ringkanalDie vorliegende Arbeit wurde von der Deutschen Forschungsgemeinschaft unter der Numraer Me 261/3 unterstützt. (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 454-479 
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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 three-dimensional perturbation flow induced by a rotating and oscillating blade row which operates in a subsonic flow in axial direction of an annular channel is studied. The velocity potential is reduced to the infinite Hilbert space vector of Fourier coefficients of an eigen-function expansion with respect to vanishing normal derivatives on both cylinder walls. These coefficients satisfy an infinite set of ordinary differential equations of second order after an application of a one-dimensional Fourier transform in axial direction.Several canonical two-part mixed boundary value problems are then investigated by reduction to “infinite two-by-two-Wiener-Hopf functional systems”. In case of strong factorizability of certain matrix-operator-valued functions on the line these systems may be solved explicitely. Criteria for the factorization are not given here.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670040130
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  • 12
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    Über die existenz und eindeutigkeit einer lösung für ein randwertproblem für eine gleichung vom gemischten typ in einem rechteck (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 510-528 
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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 a boundary value problem is studied for the equation of mixed typek(y)uxx + uyy + r(x, y)u = f(x, y) in the rectangular domain {(x, y)| -1 〈 x 〈 +1, yc 〈 y 〈 yH} with yc 〈 0, yH 〉 0, k(y) = sign y|y|m, m 〉 0 (and more generally for a function k = k(y) with k(O) = 0, k(y)y 〉 O for y ≠ O). Specific for the stated problem is that no data are prescribed on the line {(x, yc), -1 〈 x 〈 +1}. It is proved that the formulated problem is well-posed in the sense that there is at most one quasi-regular solution and that a generalized solution exists. The energy-integral-(abc-)method is used to show uniqueness and to obtain an apriori estimate for the solution of the adjoint problem whence the existence statement follows.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040133
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  • 13
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    Rounding errors in numerical solutions of two linear equations in two unknownsDedicated to Professor Wolfgang Haack on the occasion of his eightieth birthday. (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 549-571 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: New condition numbers and stability constants for the numerical behaviour of Cramer's rule and Gaussian elimination for solving two linear equations in two unknowns under data perturbations and rounding errors of floating-point arithmetic are established. By these means fundamental error estimates and stability theorems are proved. The error estimates are illustrated by a series of numerical examples.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670040135
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  • 14
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    The sommerfeld half-plane problem revisited, II the factoring of a matrix of analytic functionsThese results were announced at the XXth General Assembly of the U.R.S.I. held in Washington, D.C., August 1981. (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 14-21 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A half-plane under plane wave excitation obeys a Dirichlet boundary condition on one side and a Neumann boundary condition on the other. These boundary conditions contrast the ones used by A. Sommerfeld in his classical paper. The present problem leads to a system of integral equations of the Wiener-Hopf type which may be solved by a matrix factoring method suggested by A. E. Heins in 1950.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050103
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  • 15
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    Time-invariant uniqueness for reacting viscous fluids near chemical equilibrium (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 137-141 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A system of equations is investigated which models a reacting mixture of viscous fluids acted upon by an external body force. Through logarithmic convexity arguments the solution is shown to be unique when either the initial or the final data are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130204
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  • 16
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    Remarks on the wave front of polarization: Polarized solutions for the evolution three-dimensional Lame system (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 181-188 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Some remarks complementary to the work of N. Dencker in [1] concerning the wave front of polarization are given. The theorem due to N. Dencker about the propagation of a wave front of polarization is applied to solutions for the evolution of the three-dimensional Lame system. The propagation of polarized solutions is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130208
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  • 17
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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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    ISSN: 0170-4214
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050114
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  • 18
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    On a contact problem for a system of parabolic equations in the thermal conductivity of electric machines: II (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 249-261 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The non-linear contact problem for the parabolic system of second order in the sense of Pietrovski, which is the generalization of the problem considered in Part I (preceding paper), is formulated. The matrix of fundamental solutions for parabolic systems of second order with coefficients containing unknown functions and their first-order derivatives is constructed and used to reduce the problem to the equivalent system of integral equations which is then reduced to a system of Volterra type of the second kind. The existence of the solution of the system obtained is proved by using the Schauder fixed-point theorem.
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    URL: http://dx.doi.org/10.1002/mma.1670130306
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  • 19
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    The scattering of electromagnetic waves by a perfectly conducting infinite cylinder (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 503-518 
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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 scattering of a plane time-harmonic electromagnetic wave by a perfectly conducting infinite cylinder with axis in the direction k, where k is the unit vector along the z axis. Suppose the incident wave propagates in a direction perpendicular to the cylinder. For a given observation angle θ, let FD(θ, α)k be the far-field pattern of the electric field corresponding to an incident wave with direction angle α polarized perpendicular to the axis and let FN(θ; α)k be the far-field pattern of the magnetic field corresponding to an incident wave with direction angle α polarized parallel to the z axis. Let {αn}n=1∞ be a distinct set of angles in [ - π, π] and μ a complex number. Then, necessary and sufficient conditions are given for the set {(1 - μ)FD(θ;αn) + μFN(θ;αn)}n = 1∞ to be complete in L2[ - π, π]. Applications, together with numerical examples, are given to the inverse scattering problem of determining the shape of the cylinder from a knowledge of the far-field data.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670120605
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  • 20
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    Some solutions for the spin glass system and for systems originating from it (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 31-41 
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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 spin glass system the solutions, u = νΦ and u = νx/|x| are considered, where ν is a scalar function and Φε∝3 is constant. For a system originating from the spin glass one, a solution u = tan[q(|x|/t)]x/|x| is considered.
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    URL: http://dx.doi.org/10.1002/mma.1670130104
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  • 21
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    Masthead (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990) 
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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.1670130201
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  • 22
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    A study of a non-linear kinetic model for an ionized gas (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 95-109 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A non-linear one-dimensional kinetic model for an ionized gas is considered. In this model the collisions between charged and neutral particies and the field generated by the charges are taken into account. The Cauchy problem for the resulting system of equations is examined. An existence and uniqueness theorem of a global in time solution is proved.
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    URL: http://dx.doi.org/10.1002/mma.1670130202
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  • 23
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    A two-species plasma in the limit of large ion mass (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 159-167 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Classical solutions of the relativistic Vlasov-Maxwell system are considered, describing a collisionless plasma with two species of particles. ions and electrons. It is shown that as the ion mass m tends to infinity, the corresponding solution of the relativistic Vlasov-Maxwell system tends to the solution of a system, in which the ions are given by a fixed ion background and only the electrons move. The convergence is uniform on compact time intervals, with an asymptotic convergence rate of m-1.
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    URL: http://dx.doi.org/10.1002/mma.1670130206
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    Asymptotic analysis of the quantum Liouville equation (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 143-157 
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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 an asymptotic analysis of the quantum Liouville equation with respect to the Planck's constant, which models the temporal evolution of the (quasi)distribution of an ensemble of electrons under the action of a potential. We consider two cases: firstly a smooth potential, and secondly a potential modelled by a δ-distribution. In both cases the zeroth-order term behaves classically. In the smooth case the classical Liouville equation is satisfied and in the case for the δ-potential an interface condition is derived, so that everything is reflected at the potential barrier.
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    URL: http://dx.doi.org/10.1002/mma.1670130205
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  • 25
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    Variational derivatives and p-gradients of functionals on spaces of continuously differentiable functions (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 530-543 
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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 introduce and study a new type of derivative - the variational gradient - for a functional on Cn[a, b]. Local and global versions of this concept are analyzed. This notion provides a natural approach to variational derivatives on Cn[a, b] under rather mild smoothness assumptions on the functional. When applied in the context of the Calculus of Variations, the notion of the variational gradient captures the natural boundary conditions (as well as the Euler-Lagrange equations) under weaker smoothness assumptions than those usually required using Gǎteaux variations.Conditions are established for the existence of the variational derivative and an integral representation for the Gǎteaux variation in terms of the variational derivative is derived. Conditions for the variational derivative to be differentiable are also established.
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    URL: http://dx.doi.org/10.1002/mma.1670050132
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  • 26
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    A symmetry theorem for condensers (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 315-320 
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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 radial symmetry of the solution of degenerate quasilinear capacity problems, when constant overdetermined Neumann data are assigned.
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    Attenuation correction in positron emission tomography (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 321-330 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We describe a mathematical method for computing the attenuation distribution from Positron emission tomography (PET) data. The method renders possible the correction of PET data for attenuation without a transmission scan. It can be applied if the attenuation distribution is sufficiently simple (abdomen and bead). We give the results for computer-generated data and for data on patients.
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    On mathematical modelling of absorption and dispersion of seismic waves for low frequencies (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 563-572 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The problem of determining the dispersion and absorption of plane seismic waves by a given seismic quality factor is dealt with in the case that the quality factor tends to a positive limit as the frequency goes to zero.General formulae are derived for the phase velocity and the attenuation coefficient by solving the corresponding Riemann-Hilbert problems for analytic functions in the upper half-plane.
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    Wiener-hopf equations for waves scattered by a system of parallel sommerfeld half-planes (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 525-552 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: A scalar time-harmonic wave (governed by Helmholtz's equation) impinges on N semi-infinite half-planes. The scattered field is sought when first, second, and third-kind boundary conditions or even general linear transmission conditions on the plates ∑m and their complementary parts ∑m′ are prescribed. Making use of the Fourier transform a representation formula for H1 (Ω) solutions is presented. The boundary/transmission problem is shown to be equivalent to a (2N × 2N)-Wiener-Hopf (WH) system for jumps of the Dirichlet-and Neumann-Cauchy data across the semi-infinite screens ∑m. The (2N × 2N)-Fourier symbol matrix SP contains N block matrices on the diagonal corresponding to Sommerfeld boundary/transmission problems for a single plate. These (2 × 2)-symbol matrices are factorizable and thus the full WH system is invertible by a perturbation argument for not too small spacings of neighbouring screens ∑m.
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    Convergence analysis for a multiplicatively relaxed EM algorithm (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 573-593 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The expectation maximization (EM) algorithm is an iterative procedure used to determine maximum likelihood estimators in situations of incomplete data. In the case of independent Poisson variables it converges to a solution of a problem of the form min ∑[〈ai,x〉 - bi log 〈ai, x〉] such that x ≥0. Thus, it can be used to solve systems of the form Ax = b, x≥0 (with A stochastic and b positive.) It converges to a feasible solution if it exists and to an approximate one otherwise (the one that minimizes d (b, Ax), where d is the Kullback-Leibler information divergence). We study the convergence of the multiplicatively relaxed version proposed by Tanaka for use in positron emission tomography. We prove global convergence in the underrelaxed and unrelaxed cases. In the overrelaxed case we present a local convergence theorem together with two partial global results: the sequence generated by the algorithm is bounded and, if it converges, its limit point is a solution of the aforementioned problem.
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    A contribution to matrix equations arising in system theory (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 593-597 
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    Notes: A useful relationship between solutions is derived for a class of matrix equations arising in the system theory, particularly in the context of the orthogonal approximation of linear dynamic systems. The computational aspects of the result are discussed and illustrated on an example of practical importance.
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    Masthead (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Dynamic MRI reconstruction as a moment problem (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 661-675 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: This paper deals with some mathematical aspects of magnetic resonance imaging (MRI). MRI is used in diagnostic medicine to measure and display the cross section of, for example, a human organ. In this paper we formulate the MRI-reconstruction problem and solve it aftèr restating it as a moment problem in a Hilbert space.
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
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    Behaviour of mushy regions under the action of a volumetric heat source (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 35-47 
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    Notes: In this paper we consider solutions to Stefan problems in spatial dimensions N ≥ 1. We find the necessary conditions on the heat source for the appearance of a ‘mushy region’ (i.e. a region where the temperature coincides identically with the temperature of the change of phase) inside a purely liquid (or solid) phase. For sources depending on energy such conditions are connected only with the local behaviour of the source near the energy level corresponding to the beginning of the change or phase. Both weak and smooth solutions are considered; in the latter case the behaviour of the solution at the free boundary is investigated in detail.
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    On the asymptotic growth of the solutions of the vlasov-poisson system (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 75-85 
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    Notes: We show the global existence of classical solutions of the Vlasov-Poisson system and improve the known growth estimates.
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    Global solution to the Cauchy problem in non-linear hyperbolic thermoelasticity (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 223-237 
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    Notes: We prove the existence of global solutions for small data to the initial value problem for the non-linear hyperbolic system of partial differential equations describing a thermoelastic medium in a three-dimensional space under the assumption that the coefficients in the non-linear terms are smooth functions of their arguments and behave like 0(∣η∣k0) for k0 ≥ 2 near the origin. The asymptotic behaviour of the solution as t → ∞ is also described.
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    Masthead (1992)
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    Mathematical Methods in the Applied Sciences 15 (1992) 
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    On degenerate diffusion with very strong absorption (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 469-477 
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    Notes: We prove the existence of weak global solutions to the degenerate diffusion equation (1) with singular absorption term. Moreover we investigate the regularity up to the quenching time and we show by means of explicit solutions that our regularity results are optimal.
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    Abstract Besov space approach to the non-stationary Navier-Stokes equations (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 599-620 
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    Notes: The local existence, uniqueness and regularity of solutions of the initial-value problem for non-stationary Navier-Stokes equations are studied via abstract Besov spaces. The assumptions about Ω the initial data and the external force are improved on by rather simple proofs.
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    Multicriteria optimization in antenna design (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 647-660 
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    Notes: We formulate certain problems in the optimal design of radiating structures such as multicriteria optimization problems. We review the basic background of such problems, prove the existence of Pareto optimal points, and give necessary conditions. We apply the latter to the numerical computation of optimal surface currents for the problem of simultaneously optimizing both the quality factor and the signal-to-noise ratio of a conformal antenna.
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    High-frequency asymptotics in inverse scattering by ellipsoids (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 1-12 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: A triaxial ellipsoid of unknown position, size and orientation is located somewhere in space. High-frequency asymptotics for the scattering amplitude and the sojourn time for the travelling of a high-frequency acoustic plane wave are utilized to determine the position of a supporting plane for the ellipsoid. We describe a method that identifies the coordinates of the centre, the three semiaxes, and the three angles of the ellipsoid from the knowledge of nine sojourn times corresponding to nine directions of excitation. The method is independent of boundary conditions, it is applicable to any restricted non-zero-measure angle of observation, and leads to numerics that avoid elliptic integrals. A priori information about the location of the ellipsoid reduces the number of measurements to six, while the corresponding algorithm demands the solution of a linear system and the inversion of a dyadic.
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    Masthead (1993)
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    Mathematical Methods in the Applied Sciences 16 (1993) 
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    Schauder estimates for boundary layer potentials (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 877-894 
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    Notes: Boundary layer potentials with Hölder-continuous densities are widely used for representing solutions of boundary value problems for certain partial differential equations. These potentials are of the type with |ρ| odd and a density λ of class Ck+α. This paper presents a self-contained exposition of the fact that the potential v may be continued as Ck+α-functions onto G and ∝n\G respectively (together with estimates for the Hölder-norms) under the least possible regularity assumption for the boundary ∂G: it has to be of class Ck+1+α.
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    Beyond quenching for singular reaction-diffusion problems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1-9 
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    Notes: Let f(u) be twice continuously differentiable on [0, c]) for some constant c such that f(0) 〉 0,f′ ≥ 0,f″ ≥ 0, and limu→cf(u) = ∞. Also, let χ(S) be the characteristic function of the set S. This article studies all solutions u with non-negative ut, in the region where u 〈 c and with continuous ux for the problem: uxx - ut = - f(u)χ({u 〈 c}), 0 〈 x 〈 a, 0 〈 t 〈 ∞, subject to zero initial and first boundary conditions. For any length a larger than the critical length, it is shown that if ∫0cf(u) du 〈 ∞, then as t tends to infinity, all solutions tend to the unique steady-state profile U(x), which can be computed by a derived formula; furthermore, increasing the length a increases the interval where U(x) ≡ c by the same amount. For illustration, examples are given.
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    Approximating sequences for heteroclinic orbits (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 71-76 
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    Notes: In this paper we construct two approximating sequences for heteroclinic solution to a scalar ODE. These sequences do not ‘intersect’ and bound a unique real solution from below and above, thus enabling us to estimate this solution with any accuracy.
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    Masthead (1994)
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    Mathematical Methods in the Applied Sciences 17 (1994) 
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    The existence of solutions of a general boundary value problem for the divergence (1994)
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 95-105 
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    Notes: This paper is concerned with the question of necessary and sufficient conditions to find a vector field V∊ Γ(TM) solving the equation div V = Φ under inhomogeneous boundary conditions V|∂M = Z|∂M with Z∊ Γ (TM) An existence and regularity result is given for an arbitrary Riemannian manifold with boundary, M. The proof is based on the Hodge theory of differential forms.
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    Local compactness for linear elasticity in irregular domains (1994)
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 107-113 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: For the theory of boundary value problems in linear elasticity, it is of crucial importance that the space of vector-valued L2-functions whose symmetrized Jacobians are square-integrable should be compactly embedded in L2. For regions with the cone property this is usually achieved by combining Korn's inequalities and Rellich's selection theorem. We shall show that in a class of less regular regions Korn's second inequality fails whereas the desired compact embedding still holds true.
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    Mathematical problems of liquid crystal flows (1994)
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 171-188 
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    Notes: This article deals with flow phenomena in liquid crystal materials. The model that I analyse is that due to Ericksen for liquid crystals with variable degree of orientation. One of the goals is understanding the role of the order parameter in the model. I examine the multiplicity of solutions, phases, that occur in shear flow regimes and analyse their stability under physically realistic conditions. In particular, I show that ellipticity of the linearized system of governing equations is a consequence of the Clausius-Duhem inequality.
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    Masthead (1994)
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    Mathematical Methods in the Applied Sciences 17 (1994) 
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    Landesman-Lazer resonance problems and saddle point methods (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 229-238 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We show how saddle point techniques can be used to obtain new results for general resonance problems of the type considered by Landesman and Lazer.
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    The stationary and non-stationary stokes system in exterior domains with non-zero divergence and non-zero boundary values (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 269-291 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In an exterior domain Ω⊂∝n, n ≥ 2, we consider the generalized Stokes resolvent problem in Lq-space where the divergence g = div u and inhomogeneous boundary values u = ψ with zero flux ∫∂Ωψ·N do = 0 may be prescribed. A crucial step in our approach is to find and to analyse the right space for the divergence g. We prove existence, uniqueness and a priori estimates of the solution and get new results for the divergence problem. Further, we consider the non-stationary Stokes system with non-homogeneous divergence and boundary values and prove estimates of the solution in L5(0, T;Lq(Ω)) for 1 〈 s, q 〈 ∞.
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    Finite element approximation of a microstructure evolution (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 377-393 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The evolution model of a microstructure described as appropriately generalized Young measures, which was developed in [11], is discretized here by means of a suitably adapted finite element method. The convergence of the approximate solutions is proved, and a one-dimensional example is treated to discuss some implementation experience and to show some illustrative results.
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    Masthead (1994)
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    Mathematical Methods in the Applied Sciences 17 (1994) 
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    Weak solutions of the initial-boundary value problem for the Vlasov-Poisson system (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 451-476 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we show the existence of a weak solution of the boundary value problem for the time dependent Vlasov-Poisson system. First, we regularize the system in order to apply a fixed-point theorem. Then we pass to the limit using an energy estimate.
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    Optimal control for parabolic systems with competitive interactions (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 509-524 
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    Notes: We consider a two-dimensional parabolic system with general competitive interactions as a two-player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functional.
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    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
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    Local existence of solutions to the Landau-Maxwell system (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 613-641 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We study here the Landau-Maxwell system in its classical form. We prove the local existence of weak solution with initial data of unrestricted size. The main tools consist of an approximation method and a regularity result for velocity averages of solutions of some general linear transport equations.
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    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
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    A finite element method and stabilization method for a non-linear tricomi problem (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 681-695 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We prove using the Faedo-Galerkin method the existence of a generalized solution of an initial-boundary value problem for the non-linear evolution equation0 ≤ Q ≤ 2, in a cylinder QT = Ω × (0, T), where T u = yuxx + uyy is the Tricomi operator and l(u) a special differential operator of first order. We then show that the approximate generalized solution of problem (*) converges to the approximate generalized solution of the corresponding stationary boundary value problem as t → ∞.
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    On a semi-coercive problem in a porous journal bearing with cavitation problem as boundary condition and subject to an integral condition (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 765-785 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We study a non-linear problem in pressure saturation modelling of a free boundary problem, arising in self-lubricating bearings, with Neumann boundary conditions for the pressure and a non-local constraint on the saturation variable, which indeed is a Lagrange multiplier. We prove an existence theorem by introducing an artificial time dependence and using the pseudo-characteristics discretization method and semi-coercive variational inequalities.
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    On stationary flow of asymmetric fluids with diffusion (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 837-854 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We prove existence and uniqueness theorems for weak solutions of equations describing stationary isothermic motion of a mixture of two viscous incompressible fluids with asymmetric stress tensor, in a bounded subset of ∝3. The model of the flow we consider here assumes that some of coefficients characterizing isotropic properties of the fluid equal zero.
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    Control problems with state constraints for shape memory alloys (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 943-952 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper, two different control problems with state constraints for shape memory alloys are considered: in the non-isothermal case, we study boundary control problems, and in the isothermal situation, a dynamical shape optimization problem is considered. In both cases, the transverse displacement is the constrained state variable. The first-order conditions of optimality are derived.
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    Quantitative error estimates for coefficient idealization in linear elliptic problems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 971-987 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We give a thorough quantitative error analysis for the effect of coefficient idealization on solutions of linear elliptic boundary value problems. The a posteriori error estimate is derived by a tactful application of the duality theory in convex analysis. The estimate involves an auxiliary function subject to certain constraint. We discuss in detail the selection of a good auxiliary function for various cases. Numerical examples show the effectiveness of our a posteriori error estimate.
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    An approximate Gidas-Ni-Nirenberg theorem (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1045-1052 
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    Notes: We study positive solutions u to Δu + f(u) = 0 in Ω, u = 0 on ∂Ω, and we address the following question: If Ω is a small perturbation of a ball, is u a small perturbation of a radially symmetric function? We prove two theorems which give an affirmative answer under different assumptions on the non-linearity f and on the topologies in which perturbations are considered.
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    Diffusion limit for the linear boltzmann equation of the neutron transport theory (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1071-1087 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we present the asymptotic analysis of the linear Boltzmann equation for neutrons with a small positive parameter ∊ related to the mean free path, based upon the Chapman-Enskog procedure of the kinetic theory. We prove that if proper initial conditions derived by considering initial layer solutions are used, the diffusion equation gives the uniform approximation to the neutron density function with the O(∊2) accuracy.
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    Stability analysis of the phytoplankton vertical steady states in a laboratory test tube (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 551-575 
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    Notes: The positive vertical equilibrium profiles of a phytoplankton population growing in a vertical test tube under controlled experimental conditions (temperature, salinity, light intensity at the top surface) for nutrients are discussed with reference to their stability properties for arbitrary positive initial values of the biomass concentration along the tube. Two different approaches are followed. First a stability result is established in the Sobolev norm H2 by estimating the norms of the perturbations recursively in successive subintervals of suitably small amplitude. The second approach provides stability in the sense of the uniform convergence as a corollary of a stability theorem for a rather general class of integro-differential equations.
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    Non-linear stability for the Vlasov-Poisson system - the energy-Casimir method (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1129-1140 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The problem of stability of stationary solutions of the Vlasov-Poisson system has received a lot of attention in the physics literature, both in the stellar dynamics and the plasma physics cases. The energy-Casimir method has been used to prove non-linear stability for various conservative systems, but no rigorous application to the Vlasov-Poisson system has been given yet. We employ this method to prove non-linear stability of stationary solutions for the plasma physics case in three geometrically different settings.
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    Masthead (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990) 
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    An existence theorem for Poiseuille flow with surface tension in an open channel (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 23-30 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Poiseuille-type flow in an open channel is studied taking surface tension and wall adhesion into account. A proof is presented of the existence of a solution under certain conditions.
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    Low-frequency asymptotics for dissipative Maxwell's equations in bounded domains (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 81-93 
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    Notes: Consider a bounded domain Ω surrounded by a perfect conductor and containing a conducting cavity D. The behaviour of the solutions of the time harmonic Maxwell problem as frequency tends to 0 is analysed in this situation. Necessary and sufficient conditions on the excitations are given which guarantee the existence of a limit. This limit turns out to be the solution of some static problem.
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    Zero resonances in local perturbations of parallel-plane waveguidesHerrn Professor Rolf Leis zum 60. Geburtstag am 22·7·1991 gewidment (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 111-136 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In a joint paper with K. Morgenröther [9] we have studied the propagation of scalar waves in domains of the type Ω = Ωo-B̄ with Ωo:=∝2 × (0, 1), where B is a smooth bounded domain with B̄ ⊏ Ωo. In particular, we have shown that the solution of Neumann's initial and boundary value problem for the wave equation with time-independent right-hand side ƒ increases with a logarithmic rate as t → ∞ if the integral over ƒ does not vanish. The main purpose of the present paper is to extend this result to arbitrary smooth local perturbations of Ωo.
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    On the ‘one and one-half dimensional’ relativistic Vlasov-Maxwell system (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 169-179 
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    Notes: The time evolution of a collisionless plasma is studied in the case when the Viasov density ƒ is a function of the time, one space variable and two velocity variables. The electromagnetic fields E, B also have a special structure, and the magnetic field B is non-trivial. It is shown that smooth, consistent initial values generate a uniquc smooth global solution.
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    On the uniqueness of motion of viscous gaseous stars (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 391-404 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The existence of solutions of the evolutionary equations of motion of a star regarded as a compressible viscous fluid with self-gravitation, bounded by a free surface, has recently been considered [3, 4]. In this paper I study the uniqueness of the above solutions.
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    An optimal control problem for the Helmholtz equation in a stratified Shallow oceanThis research was supported in part by the U.S. AFOSR86-0269. (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 405-419 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we shall consider a kind of optimal control of the Robin problem. First, we discuss the solvability of the Robin problem, which is not uniquely solvable in general. Then we find the representation of the far-field pattern in terms of the minimal solution to an integral equation. Based on this representation, an optimization problem is discussed and a Galerkin scheme for the solution is presented.
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    Higher moments for kinetic equations: The Vlasov-Poisson and Fokker-Planck cases (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 441-452 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Let us consider a solution f(x,v,t)∊L1(∝2N × [0,T]) of the kinetic equation where |v|α+1 fo,|v|α ∊L1 (∝2N × [0, T]) for some α〈 0. We prove that f has a higher moment than what is expected. Namely, for any bounded set Kx, we haveWe use this result to improve the regularity of the local density ρ(x,t) = ∫ƒdν for the Vlasov-Poisson equation, which corresponds to g = Eƒ, where E is the force field created by the repartition ƒ itself. We also apply this to the Bhatnagar-Gross-;Krook model with an external force, and we prove that the solution of the Fokker-Pianck equation with a source term in L2 belongs to L2([0, T]; H1/2(∝x,v2N)).
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    On the mathematical foundations of hyperthermia therapy (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 467-479 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Hyperthermia is an aid to standard cancer therapy. The aim is to heat up a tumour region inside the patient's body with the help of microwave radiation. The microwayes are generated by some suitable antenna array. Here we investigate the control properties of such antenna configurations and determine their resolution capabilities. We will define the hyperthermia operator, which can produce every field of any antenna array up to any degree of accuracy. We shall see that this operator is compact and we are able to compute a singular system under general assumptions explicitly. This, together with a detailed knowledge of the decay of the singular values, constitutes the tools with which we treat the previously stated problems. We examine the propagation of microwave radiation in homogeneous media and then carry over the results obtained to the case of inhomogeneous media.
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    Non-homogeneous non-linear damped wave equations in unbounded domainsSupported by the SFB 256 of the Deutsche Forschungsgemeinschaft at the University of Bonn, F.R.G. (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 481-491 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We present a global existence theorem for solutions of utt - ∂iaik (x)∂ku + ut = ƒ(t, x, u, ut, ∇u, ∇ut, ∇2u), u(t = 0) = u0, ut(=0)=u1, u(t, x), t ⋝ 0, x∊Ω.Ω equals ∝3 or Ω is an exterior domain in ∝3 with smoothly bounded star-shaped complement. In the latter case the boundary condition u|∂Ω = 0 will be studied. The main theorem is obtained for small data (u0, u1) under certain conditions on the coefficients aik.The Lp - Lq decay rates of solutions of the linearized problem, based on a previously introduced generalized eigenfunction expansion ansatz, are used to derive the necessary a priori estimates.
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    The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 35-61 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We prove the existence of a unique, global classical solution of the quantum Vlasov-Poisson problem posed on the phase space ∝x3 × ∝v3. The proof is based on a reformulation of the quantum Vlasov-Poisson problem as a system of countably many Schrödinger equations coupled to a Poisson equation for the potential. The Schrödinger-Poisson problem is first analysed on a bounded domain in ∝x3 and the solution of the whole-space problem is then obtained by a limiting procedure in which the domains ‘tend’ to ∝x3.
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    Dynamical shape control and the stabilization of non-linear thin rods (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 63-78 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we consider the problem of stabilizing the motion of the tip of a thin rod by controlling the shape of the rod, that is its length, dynamically. Well-posedness of the associated state equations, valid on a moving domain, is proved, and the necessary conditions of optimality for the control problem are derived. The theory applies to materials where the stress-strain relation is both non-linear and non monotone, so that hysteresis effects arising from solid-solid phase transitions in the rod are included.
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Entropy compactification in Lagrangean gas dynamics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 207-216 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    An approximation of the thermal field in a continuous casting process of a thin metal layer (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 217-226 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We consider the problem of a phase change in a continuous casting process: molten bronze is poured on to a moving steel strip cooled from below, in order to solidify the bronze. An estimate of the width of the solidification zone, depending on the thickness of the strip and on the casting velocity, is obtained, neglecting conduction in the direction of the strip motion.
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    The problem of equivalence in statistical mechanics of equilibrium (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 319-331 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The physical problem of the equivalence of certain partition function in statistical mechanics leads to the following mathematical problem: Under what conditions is the logarithm of a Laplace-Stieltjes transform of the so-called microcanonical partition function equal to a Legendre transform of the logarithm of the latter? The conditions we shall formulate turn out to be physically reasonable.
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    Charge transport in semiconductors with degeneracy effects (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 301-318 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It has been a common procedure to derive a model for charge transport in degenerate semiconductor material by incorporating a Fermi-Dirac distribution into the classical drift-diffusion model. In this work a Boltzmann equation with a non-linear collision term is considered. A new fluid dynamical model is derived by considering small perturbations of the thermal equilibrium. The analysis contains an existence and uniqueness proof for the Boltzmann equation, a justification of the perturbation argument and a study of initial boundary value problems for the new fluid dynamical model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140503
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    Asymptotic completeness in optical scattering (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 333-354 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper time-dependent methods are developed in order to prove the existence of the wave operators and asymptotic completeness in the scattering theory of electromagnetic waves in inhomogeneous media.The medium has a localized perturbation of the dielectric susceptibility. There are no regularity assumptions about the dielectric susceptibility.It is shown directly that the range of the wave operator is the complete continuous subspace, and not just the absolutely continuous subspace of the generator of the time evolution describing the perturbed wave propagation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140505
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    On the linear piezoelectricity of composite materials (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 403-412 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: From the equations of the linear piezoelectricity for a composite material with a periodic structure we derive the dynamical solution by means of Bloch expansion techniques. This expression techniques. This expression allows, as a limit case, a comparison with the homogenization method, and the macroscopic coefficients are also deduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140604
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    An integral operator related to the stokes system in exterior domains (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 445-445 
    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.1670140608
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
    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.1670140801
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  • 92
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    Generalized limiting absorption method and multidimensional inverse scattering theory (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 509-524 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We generalize the classical limiting absorption method. This generalization is applied to the study of the Faddeev-Lippmann-Schwinger equations in the Faddeev-Newton approach to multidimensional inverse scattering theory. In particular, we give a new proof, under more general conditions than were known previously, of the absence of exceptional points for small potentials and large values of the parameters, and on the existence of real exceptional points if there are complex ones, in particular for potentials that produce negative eigenvalues.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140705
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    The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 595-613 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the global existence of a unique classical solution of the two-dimensional Wigner-Poisson problem by a reformulation as a system of countably many Schrödinger equations coupled to a Poisson equation. The charge neutrality of the system implies the boundedness of the electrostatic potential in two dimensions, which is an important ingredient for the proof.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140902
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    Inversion of the Radon transform with incomplete data (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 159-166 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Radon transform R(p, θ), θ∊Sn-1, p∊∝1, of a compactly supported function f(x) with support in a ball Ba of radius a centred at the origin is given for all \documentclass{article}\pagestyle{empty}\begin{document}$ \theta \in \mathop {S^{n - 1} }\limits^\tilde $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {S^{n - 1} }\limits^\tilde $\end{document} is an open set on Sn-1, and all p∊(- ∞, ∞), n≥2. An approximate formula is given to calculate f(x) from the given data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670150303
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    Masthead (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992) 
    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.1670150401
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    Pseudodifferential operators with real analytic symbols and approximation methods for pseudodifferential equationsDedicated to Professor Rudolf Gorenflo on the occasion of his sixtieth birthday. (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 239-264 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper introduces some methods (including an approximation method) for investigating pseudodifferential equations and related problems (Cauchy problems, boundary value problems,…) based on the technique of pseudodifferential operators with real analytic symbols.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670150403
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    Properties of solutions to the initial-boundary value problem for a porous media-type equation (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 299-314 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The initial-boundary value problem in a semi-infinite strip (0, ∞)×(0, T) for a degenerate parabolic equation of the form u, t= ϕ(u)xx + b(x)ϕ(u)x is considered. The properties of solutions in the case where the initial function is compactly supported and for constant initial and boundary data are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670150502
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    Masthead (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992) 
    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.1670150601
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    A non-isentropic Euler-Poisson model for a collisionless plasma (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 409-442 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We analyse transonic solutions of the one-dimensional Euler-Poisson model for a collisionless gas of charged particles in the non-isentropic steady-state case. The model consists of the conservation of mass, momentum and energy equations. The electric field is modelled self-consistently (Coulomb field). Boundary conditions on the particle density and particle temperature are imposed.The analysis is based on representing solutions piecewise as orbits in the particle-density-electric-field phase plane and connecting the orbit segments by the jump and entropy conditions.We characterize the set of all solutions of the Euler-Poisson problem. In particular, we show that, depending upon the length of the interval on which the boundary value problem is posed, fully subsonic, one-shock and (in certain cases) two-shock transonic and smooth transonic solutions exist. Also, numerical computations illustrating the structure of the solutions are reported.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160603
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    Resonance phenomena in a semi-infinite string with a periodic end (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 501-531 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in a semi-infinite string under the assumption that the material properties depend p-period-ically on the space variable outside a sufficiently large interval [0, a]. The spectrum of the self-adjoint extension A of the spatial part of the differential operator consists of a finite or countable number of bands and a (possibly empty) discrete set of eigenvalues located in the gaps of the continuous spectrum. We show that resonances of order t or t½, respectively, occur if either ω2 is an eigenvalue of A or (i) ω2 is a boundary point of the continuous spectrum of A and (ii) the corresponding time-independent homogeneous problem has a non-trivial solution which is p-periodic or p-semiperiodic for x 〉 a (‘standing wave’).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160704
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