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  • Mathematics and Statistics  (340)
  • Wiley-Blackwell  (340)
  • Copernicus
  • 1985-1989  (340)
  • 1
    Electronic Resource
    Electronic Resource
    On the low wave number asymtotics for the two-dimensional exterior dirichlet problem for the reduced wave equationDedicated to E. Martensen on the occasion of his 60th birthday (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 335-341 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new proof is given for the low wave number asymptotics for the solutions to the exterior Dirichlet problem for the reduced wave equation in two dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090126
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  • 2
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    Diffraction d'une Onde Acoustique par une Paroi Absorbante: Nouvelles Equations Intégrales (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 431-454 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present here a new formulation of the exterior Robin problem of the reduced wave equation, using boundary integrals with the jumps of the function and its normal derivative as variables. Our system of integral equations present an important advantage for any numerical purpose: it can be transformed in a variational problem where the sesqui-linear form is coercive and is exempt of hyper singular integrals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090131
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  • 3
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    An integral equation of the first kind for a free boundary value problem of the stationary Stokes' equations (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 550-575 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate a free boundary value problem of the stationary Stokes' equations. In a previous paper adapted hydrodynamical potentials have been constructed and their jump relations have been discussed. Here we study a direct method to obtain an equivalent boundary integral equations' system of the first kind. Its solution properties are investigated in the framework of strongly elliptic pseudodifferential operators. For numerical purposes a suitable representation formula for the variational equation is given in terms of integro-differential operators which avoids the evaluation of hypersingular integrals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090135
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  • 4
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    Masthead (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988) 
    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.1670100101
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  • 5
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    Explicity resolvable equations with functional non-linearities (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 477-485 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the non-linear evolution equation μdu/dt+Bu+n(u)L(u)=h, where n(u) is a functional, and introduce assumptions which allow its explicit solution. Several concrete applications of our procedure are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100411
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  • 6
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    Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 197-223 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a thermomechanical model for the dynamics of structural phase transitions in the so-called ‘shape memory alloys’ is developed. These materials exhibit rather spectacular hysteresis phenomena. The resulting mathematical model consists of a coupled and highly non-linear system of partial differential equations reflecting the balance laws of linear momentum and energy. For an appropriate weak formulation the local-in-time existence of weak solutions is shown.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100302
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  • 7
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    Explicit formula for scalar non-linear conservation laws with boundary condition (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 265-287 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove an uniqueness and existence theorem for the entropy weak solution of non-linear hyperbolic conservation laws of the form \documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{\partial }{{\partial t}}u + \frac{\partial }{{\partial x}}f\left(u \right) = 0 $$\end{document}, with initial data and boundary condition. The scalar function u = u(x, t), x 〉 0, t 〉 0, is the unknown; the function f = f(u) is assumed to be strictly convex. We also study the weighted Burgers' equation: α ∊ ∝ \documentclass{article}\pagestyle{empty}\begin{document}$$ \frac{\partial }{{\partial t}}\left({x^\alpha u} \right) + \frac{\partial }{{\partial x}}\left({x^\alpha \frac{{u^2 }}{2}} \right) = 0 $$\end{document}.We give an explicit formula, which generalizes a result of Lax. In particular, a free boundary problem for the flux f(u(.,.)) at the boundary is solved by introducing a variational inequality. The uniqueness result is obtained by extending a semigroup property due to Keyfitz.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100305
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  • 8
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    Masthead (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988) 
    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.1670100401
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  • 9
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    Unilateral contact with adherence (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 367-381 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The dissipative adhesive properties of a viscoelastic solid are investigated. An approximate problem is considered and an existence theorem is proved. Numerical computations are presented.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100403
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  • 10
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    A dual method to the collocation method (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 439-445 
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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 article we consider methods which are related to the collocation method by interchanging the test and the trial spaces. Error estimates are derived. As a by-product we obtain some extensions to the known convergence results for the collocation method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100408
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  • 11
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    A stability result for distributed parameter identification in bilinear systems (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 447-456 
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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 stability result for the problem of identifying distributed parameters (for instance, a conductivity matrix) in partial differential equations. The result is used to establish an error estimate for an algorithm to identify the parameter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100409
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  • 12
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    Time-periodic solutions of wave equations on ∝1 and ∝3 (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 457-475 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The classical Paiey-Wiener theorem and Hilbert space methods are used to show the existence of time-periodic solutions of the wave equation wtt-wrr+λw=h, 0 〈 r 〈 + ∞, which are radially symmetric and have exponential decay as r → + ∞. This problem is obtained when considering a one-dimensional or three-dimensional problem, and should be thought of as a linearization of a semilinear problem in which the associated linear operator has point spectrum (- ∞, λ). When λ ≤ 0 there is uniqueness, otherwise there is a non-trivial finite-dimensional null space. Estimates on w, wt, wr are obtained, which show that in either case there is a continuous correspondence h → w, where w is a uniquely characterized solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100410
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  • 13
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    Unique continuation for Schrödinger operators and for higher powers of the Laplacian (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 531-542 
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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 unique continuation property for Schrödinger operators and its application for proving the non-existence of positive eigenvalues (embedded in the continuous spectrum). We also use the estimate given by Jerison and Kenig9 to prove unique continuation for higher powers of the Laplace operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100504
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  • 14
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    The optimal stability estimate for some ill-posed Cauchy problems for a parabolic equation (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 575-583 
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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 non-characteristic Cauchy problem ut-a(x)uxx-b(x)ux-c(x)u = 0, x ∊ (0, l), t ∊ I, u(0, t) = ϕ(t), ux(0, t) = 0, t ∊ I, where I = ∝ or I = ∝+ and u(x, 0) = 0, x ∊ [0, l], in the case I = ∝+. Assuming an a priori bound for ‖u(l,.)‖L2, we derive the exact Hölder type dependence of on ‖u(x,.)‖L2 on ‖ϕ‖L2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100507
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  • 15
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    Inequalities related to stationary flows of granulated media (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 27-41 
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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 variational inequalities associated with the equations of the stationary motion of granulated media with a constant density. These inequalities replace the usual equations of motion in the case when some additional constraints are imposed on the flow.We prove the existence of solutions of the inequalities, study their regularity, uniqueness, dependence on data and relations to solutions of the equations of motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110102
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  • 16
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    Some remarks on Saint-Venant's principle (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 71-77 
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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 a three-dimensional hyperelastic cylinder in Ω = D × [0, ∞]. We study the asymptotic behaviour of the deformations of the cross-sections in an equilibrium state. In this case we show that the solutions either have exponential decay or exponential growth. We give some initial conditions such that the latter case occurs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110105
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  • 17
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    On the continuation for variational inequalities depending on an eigenvalue parameter (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 95-104 
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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 generalize recent theoretical results on the local continuation of parameter-dependent non-linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non-linear beam.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110107
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  • 18
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    Existence result and discontinuous finite element discretization for a plane stresses Hencky problem (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 169-184 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We hereafter propose and analyse a discontinuous finite element method for a plane stress Hencky problem. For that purpose we begin by proving an existence result for the continuous problem. A kind of Green's formula between \documentclass{article}\pagestyle{empty}\begin{document}$$ BD\left(\Omega \right) = \left\{{u \in {\rm{L}}^1 \left(\Omega \right),\varepsilon _{ij} (u) \in M_1 \left(\Omega \right)} \right\}{\rm{and}}H\left(\Omega \right) = \left\{{\sigma \in L^\infty \left(\Omega \right),div\sigma \in {\rm{L}}^2 \left(\Omega \right)} \right\} $$\end{document} and other intermediate results that may be of independent interest are presented and established separately. Then we formulate the discretized problem, give an existence result for it and prove a result of weak convergence of a subsequence of discrete solutions to a solution of the continuous problem.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110202
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  • 19
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    Quasilinear hyperbolic-hyperbolic singular perturbation problem: Study of shock layer (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 237-252 
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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 the asymptotic analysis of a quasilinear hyperbolic-hyperbolic singular perturbation problem in one dimension. The leading part of the analysis concerns the construction of some shock layers associated with discontinuities of a hyperbolic problem. This study is a generalization of the case of viscous perturbation for a hyperbolic problem.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110205
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  • 20
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    Anisotropic Hele-Shaw flows (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 417-429 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The procedure of Elliott and Janovsky is abstracted to a fairly general variational problem. As an application of the methodology a non-isotropic Hele-Shaw flow is treated.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110401
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  • 21
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    A penalty approximation for a unilateral contact problem in non-linear elasticity (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 447-458 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Using Ball's approach to non-linear elasticity, and in particular his concept of polyconvexity, we treat a unilateral three-dimensional contact problem for a hyperelastic body under volume and surface forces. Here the unilateral constraint is described by a sublinear function which can model the contact with a rigid convex cone. We obtain a solution to this generally non-convex, semicoercive Signorinin problem as a limit of solutions of related energy minimization problems involving friction normal to the contact surface where the friction coefficient goes to infinity. Thus we extend an approximation result of Duvaut and Lions for linear-elastic unilateral contact problems to finite deformations and to a class of non-linear elastic materials including the material models of Ogden and of Mooney-Rivlin for rubberlike materials.Moreover, the underlying penalty method is shown to be exact, that is a sufficiently large friction coefficient in the auxiliary energy minimization problems suffices to produce a solution of the original unilateral problem, provided a Lagrange multiplier to the unilateral constraint exists.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110403
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  • 22
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    Stationary solutions of the non-linear Boltzmann equation in a bounded spatial domain (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 471-481 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A contraction mapping (or, alternatively, an implicit function theory) argument is applied in combination with the Fredholm alternative to prove the existence of a unique stationary solution of the non-linear Boltzmann equation on a bounded spatial domain under a rather general reflection law at the piecewise C1 boundary. The boundary data are to be small in a weighted L∞-norm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110405
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  • 23
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    On subsolutions of a non-linear diffusion problem (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 409-416 
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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 subsolution of a non-linear diffusion problem in the radial case is constructed. Some integral equation methods are used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110308
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  • 24
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    Three-dimensional stochastic vortex flows (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 431-445 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We discuss the stochastic structure of the Navier-Stokes flow in ∝3 and prove that it can be approximated by means of a finite-dimensional stochastic process. Such a process reduces to an algorithm already discussed in Reference 4 for the Euler case, when the viscosity coefficient vanishes.
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    URL: http://dx.doi.org/10.1002/mma.1670110402
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  • 25
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    Boundary control of a vibrating plate with internal damping (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 573-586 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that finite energy states of a vibrating viscoelastic plate of the Kelvin-Voigt type are, in general, not exactly controllable by L2-boundary controls. Accordingly, we present a result on approximative controllability. The method is general.
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    URL: http://dx.doi.org/10.1002/mma.1670110502
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  • 26
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    Resonance phenomena for a class of partial differential equations of higher order in cylindrical waveguides (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 697-723 
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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 a domain Ω in ∝n of the form Ω = ∝l × Ω′ with bounded Ω′ ⊂ ∝n-l. In Ω we study the Dirichlet initial and boundary value problem for the equation ∂t2 u + [(- ∂12 -… - ∂l2)m + (- ∂l+12 -… - ∂n2)m]u = fe-iωt. We show that resonances can occur if 2m ≥ l. In particular, the amplitude of u may increase like tα (α rational, 0〈α〈1) or like in t as t∞∞. Furthermore, we prove that the limiting amplitude principle holds in the remaining cases.
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    URL: http://dx.doi.org/10.1002/mma.1670110601
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  • 27
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    Surface gradients and continuity properties for some integral operators in classical scattering theory (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 789-804 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The surface gradients of some of the most important boundary integral operators for the time-harmonic Helmholtz and Maxwell equations are computed. These results are used to give new and elementary proofs of the continuity properties of these boundary operators in Sobolev and Hölder spaces of arbitrary order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110605
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  • 28
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    Duality theorems in some overdetermined boundary value problems (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 805-819 
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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 several elliptic boundary value problems for which there is an overspecification of data on the boundary of the domain. After reformulating the problems in an equivalent integral form, we use the alternate integral formulation to deduce that if a solution exists, then the domain must be an N-ball. Various Green's functions and classical boundary value problems of second, fourth and higher order are included among the problems considered here.
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    URL: http://dx.doi.org/10.1002/mma.1670110606
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  • 29
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    Optimal bounds for bilinear forms associated with linear equations (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 518-531 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The construction of upper and lower bounds to the bilinear quantity g0, f, where f is the solution of an operator equation Tf = f0, requires either an approximation for f or one for T-1. In this paper the question of “best” approximation of T-1 by an operator of the form B = βI, where β is a real constant, is investigated for linear operators that are either self-adjoint or can be related by suitable manipulations to others that are. Particular attention is paid to a special operator, previously studied by Robinson, of importance in predicting the dynamic polarisabilities of quantum-mechanical systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070137
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    Wall effects on the slow steady motion of a particle in a viscous incompressible fluid (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 23-40 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper, asymptotic expansions with respect to small Reynolds numbers are proved for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid past a single plane wall. The flow problem is modelled by a certain boundary value problem for the stationary, nonlinear Navier-Stokes equations. The coefficients of these expansions are the solutions of various, linear Stokes problems which can be constructed by single layer potentials and corresponding boundary integral equations on the boundary surface of the particle. Furthermore, some asymptotic estimates at small Reynolds numbers are presented for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid between two parallel, plane walls and in an infinitely long, rectilinear cylinder of arbitrary cross section.In the case of the flow problem with a single plane wall, the paper is based on a thesis, which the author has written under the guidance of Professor Dr. Wolfgang L. Wendland.
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    Local existence of solutions of the vlasov-maxwell equations and convergence to the vlasov-poisson equations for infinite light velocity (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 533-558 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We prove the local existence of smooth solutions for the Vlasov-Maxwell equations in three space variables. The existence time for such solutions is independent of the light velocity c. Then we derive regularity results for both the Vlasov-Poisson and the Vlasov-Maxwell equations. The last part of the paper is devoted to a proof of weak and strong convergence of the Vlasov-Maxwell equations towards the Vlasov-Poisson equations, when the light velocity c goes to infinity.
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    Uniqueness for structural phase transitions in shape memory alloys (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 145-151 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The non-linear coupled equations arising from alloy mechanism \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {u_{tt} - a\left({u_x,\theta } \right)u_{xx} - \mu u_{xxt} - b\left({u_x,\theta } \right)\theta _x = f\left({x,t} \right),} \\ {c\left({u_x,\theta } \right)\theta _t - k\theta _{xx} - \alpha k\theta _{xxt} - \mu u_{xt}^2 - d\left({u_x,\theta } \right)u_{xt} = \lambda \left({x,t} \right),} \\\end{array} $$\end{document} have two important features: a may take negative values and c may be degenerate.The local existence has been proved in Reference 1, but the uniqueness was open. In this paper the uniqueness is proved. For a discussion of the physical model and for the justifications of the detailed technical assumptions to be made, we refer to Reference 1.
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    The capillary contact angle, II: The inclined plane (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 165-196 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In an earlier paper an hypothesis on the nature of the forces resisting motion of a liquid drop on a support surface II was introduced and tested in the (rotationally symmetric) case for which ll is a horizontal plane. In the present work II is chosen as an inclined plane, so that rotational symmetry fails. The hypothesis leads to a formal series development; in a restricted case the result is verified by a perturbation analysis, which yields the identical series.The series predictions are compared with results of computer calculations. A consequence of the analysis is an estimate for a Bohd number B0, such that a further increase in B would result in the fluid penetrating the support surface; thus an absolute upper bound B0, for stability of the envisaged configuration is obtained.
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    A free boundary problem of biological interest (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 79-93 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: During fertilization of certain echinoderms, a long actin-filled tube is extended by the sperm towards the interior of the egg. This yields a parabolic free boundary problem, which differs from the classical one-phase Stefan problem by the presence of a convective term in the partial differential equation, and because the equilibrium interface condition θ(s(t),t) = 0 is here replaced by a kinetic law s′(t) = vθ(s(t),t). This problem is set in variational form and the existence of a solution is proved by means of a Faedo-Galerkin approximation procedure.
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    Multiple scales expansions for eddy current computation in layered media (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 125-138 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: An asymptotic expansion is derived by the multiple scales method for the electromagnetic potential in a one-dimensional model problem for eddy current computations in periodic non-homogeneous layered media in presence of an integral constraint for each period.Error estimates for approximations with partial sums of any order are established. Numerical computations of correctors up to the fourth order are performed and the results are compared with the exact solution in some significant cases.
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    General conical singularities in three-dimensional Poisson problems (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 215-235 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Additional Material: 14 Ill.
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    Stability of linear systems of differential equations with variable structure and impulse effect (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 271-278 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In the present paper sufficient conditions for stability of the solutions of linear systems of differential equations with variable structure and impulse effect are found.
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    Continuous dependence on the time and spatial geometry for the equations of thermoelasticity (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 317-329 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we establish the stability of the solution of the standard initial-boundary value problem of linear anisotropic thermoelasticity under perturbations of the initial time geometry and of the spatial geometry. This is done by deriving appropriate explicit a priori inequalities which permit us to bound in particular the L2 integral of the perturbation in terms of some well defined measure of the perturbation in the geometry.
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    Finite elements for the eigenvalue problem of differential operators in unbounded intervals (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 1-39 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The eigenvalue problem for one-dimensional differential operators with a possible essential spectrum is discretized with finite elements defined on a bounded interval together with a fundamental system of the differential equation outside of the interval. A non-pollution property of the discrete spectra is proved and the error in the approximation of isolated eigenvalues and corresponding eigenvectors is estimated. The convergence of some numerical algorithms for the solution of the subsequent discrete nonlinear eigenvalue problem is proved. The method is tested in some numerical examples.
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    On spline collocation methods for boundary integral equations in the plane (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 74-89 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Nowadays boundary elemen; methods belong to the most popular numerical methods for solving elliptic boundary value problems. They consist in the reduction of the problem to equivalent integral equations (or certain generalizations) on the boundary Γ of the given domain and the approximate solution of these boundary equations. For the numerical treatment the boundary surface is decomposed into a finite number of segments and the unknown functions are approximated by corresponding finite elements and usually determined by collocation and Galerkin procedures. One finds the least difficulties in the theoretical foundation of the convergence of Galerkin methods for certain classes of equations, whereas the convergence of collocation methods, which are mostly used in numerical computations, has yet been proved only for special equations and methods.In the present paper we analyse spline collocation methods on uniform meshes with variable collocation points for one-dimensional pseudodifferential equations on a closed curve with convolutional principal parts, which encompass many classes of boundary integral equations in the plane. We give necessary and sufficient conditions for convergence and prove asymptotic error estimates. In particular we generalize some results on nodal and midpoint collocation obtained in [2], [7] and [8].The paper is organized as follows. In Section 1 we formulate the problems and the results, Section 2 deals with spline interpolation in periodic Sobolev spaces, and in Section 3 we prove the convergence theorems for the considered collocation methods.
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    A method of iterative data refinement and its applications (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 108-123 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Iterative data refinement (IDR) is a general procedure for producing a sequence of estimates of the data that would be collected by a measuring device which is idealized to a certain extent, starting from the data that are collected by an actual measuring device. Following a discussion of the fundamentals of IDR, we present a number of previously published procedures which are special cases of it. We concentrate on examples from medical imaging. In particular, we discuss beam hardening correction in x-ray computerized tomography, attenuation correction in emission computerized tomography, and compensation for missing data in reconstruction from projections. We also show that a standard method of numerical mathematics (the parallel chord method) as well as a whole family of constrained iterative restoration algorithms are special cases of IDR. Thus IDR provides a common framework within which a number of originally different looking procedures are presented and discussed. We also present a result of theoretical nature concerning the initial behavior of IDR.
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    Zur Asymptotik der wellengleichung und der wärmeleitungsgleichung in zweidimensionalen außenräumenHerrn Professor Claus Müller zum 65. Geburtstag am 20. 2. 1985 gewidmet. (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 170-201 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We study initial and boundary value problems for the wave equation and the heat equation with a time-independent right-hand term f in two space dimensions in the exterior of a closed curve C. In the case of Neumann's boundary condition ∂u/∂n = 0 on C, the solutions increase with a logarithmic rate as t → ∞ if ∫ fdx ≠ 0. In contrast to this, the solutions of the corresponding Dirichlet problems converge to the solution of the related static problem as t → ∞. In the case of the wave equation, these results have already been obtained by L: A. Muravei under the additional assumption that the curvature of C is positive, by using high frequency estimates for the reduced wave equation Δ U + ϰ2 U = 0. The analysis presented here is based on different methods, which can be applied to arbitrary smooth curves.
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    Asymptotic analysis of differential-delay equations and nonuniqueness of periodic solutions (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 223-237 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We study the differential-delay equation x′(t) = -αf(x(t-1)), where α is a positive parameter and f is an odd function which decays like x-r at infinity. In particular, we consider the case r ≤ 2, and prove the existence of periodic solutions with special symmetries which are different from previously known periodic solutions of minimal period 4. For r = 2 we prove sharp asymptotic estimates for the minimal periods of these solutions.Our results disprove a conjecture of R. D. Nussbaum.
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    An integral equation of elasticity (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 261-268 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this work a certain mixed problem in R+3 for the Lamé equations in the theory of elasticity is reduced to the integral equationAn explicit formula for the solutions is given for either Ω = {x:x2 〉 0} or Ω = {x:∥x∥〈r}. The question of smoothness of the solutions is also discused. Another formulae on Ω = {x:∥x∥〈r} are found in [5], [4]. It seems that the techniques used below allows a deeper investigation of properties of the solutions to problem (*).
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    Addendum (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 330-331 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Relative influence of two small parameters in non uniformly elliptic homogenization problems (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 367-381 
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    Notes: We study three elliptic problems depending on two small parameters (∊ = homogenization parameter and δ = perturbation parameter which causes non uniform ellipticity). In each case, the homogenized operator corresponding to the second order operator is independent of the way (∊, δ) → (0, 0), but the convergence results and the limit solution do depend on the relative size of ∊ and δ; the relevant parameter is δ∊-2.
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    Stable methods for an inverse problem in acoustic scattering by an obstacle and an inhomogeneous medium (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 385-415 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We consider (in two-dimensional Euclidean space) the scattering of a plane, time-harmonic acoustic wave by an inhomogeneous medium Ω with compact support and a bounded obstacle D lying completely outside of the inhomogeneous medium. We show that one may determine the shape of D and the local speed of sound in Ω from a knowledge of the asymptotic behavior of the scattered wave (i.e. the far field). This is done by considering a constrained optimization problem and employing integral equation and conformal mapping techniques.By assuming a priori that the functions which determine the shape of D and the local speed of sound in Ω lie in given compact sets, we show that the problem is stable, in the sense that the solution of the inverse scattering problem depends continuously on the far field data.
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    On the absolutely continuous spectrum of MHD plasma confined in the flat torus (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 432-442 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The spectral properties of the linearized MHD operator are investigated applying the theory of trace class perturbation. Especially, it is shown that the essential spectrum in the positive (stable) part of the spectrum contains the absolutely continuous one and the corresponding part of the spectrum is unitarily equivalent to some multiplication operator.
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    The exterior dirichlet problem for the Laplace equation (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 461-469 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Using a standard application of Green's theorem, the exterior Dirichlet problem for the Laplace equation in three dimensions is reduced to a pair of integral equations. One integral equation is of the second kind and the other is of the first kind. It is known that the integral equation of the second kind is not uniquely solvable, however, it has been demonstrated that the pair of integral equations has a unique solution. The present approach is based on the observation that the known function appearing in the integral equation of the second kind lies in a certain Banach space E which is a proper subspace of the Banach space of continuous complex-valued functions equipped with the maximum norm. Furthermore, it can be shown that the related integral operator when restricted to E has spectral radius less than unity. Consequently, a particular solution to the integral equation of the second kind can be obtained by the method of successive approximations and the unique solution to the problem is then obtained by using the integral equation of the first kind. Comparisons are made between the present algorithm and other known constructive methods. Finally, an example is supplied to illustrate the method of this paper.
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    Masthead (1986)
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    Mathematical Methods in the Applied Sciences 8 (1986) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    On a free boundary value problem of physical geodesy, II (existence)This paper is part of the author's “Habilitationsschrift”, accepted by the “Fachbereich 6 der Universität - Gesamthochschule - Essen”. (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 1-22 
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    Notes: The determination of the figure of the earth is considered as a local free boundary value problem of potential theory. In the C1,ε-topology local existence is proved by means of Legendre transforms. This method also provides an elementary argument for the regularity of the solutions.
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    An optimal design problem for submerged bodies (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 50-76 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The problem of finding the shape of a smooth body submerged in a fluid of finite depth which minimizes added mass or damping is considered. The optimal configuration is sought in a suitably constrained class so as to be physically meaningful and for which the mathematical problem of a submerged body with linearized free surface condition is uniquely solvable. The problem is formulated as a constrained optimization problem whose cost functional (e.g. added mass) is a domain functional. Continuity of the solution of the boundary value problem with respect to variations of the boundary is established in an appropriate function space setting and this is used to establish existence of an optimal solution. A variational inequality is derived for the optimal shape and it is shown how finite dimensional approximate solutions may be found.
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    The two-dimensional, linear, orthotropic plate: The traction problem (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 102-116 
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    Notes: In [13] we extended the analysis of Ciarlet and Destuynder [5] to the clamped orthotropic plate. For the present paper we shall apply these methods to the orthotropic plate under traction. In particular, we shall be considering the type of problem posed in Friedrichs and Dressler [10] for the isotropic plate and make use of the fact that the variational problem will split just as was the case for the partial differential equation formulation. With the present approach we shall be able to produce a proper convergence analysis for the formal asymptotics used in Friedrichs and Dressler.
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    On optimal shape design of systems governed by mixed Dirichlet-Signorini boundary value problems (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 157-181 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: A problem for finding optimal shape for systems governed by the mixed unilateral boundary value problem of Dirichlet-Signorini-type is considered. Conditions for the solvability of the problem are stated when a variational inequality formulation and when a penalty method is used for solving the state problem in question. The asymptotic relation of design problems based on these two formulations is presented. The optimal shape design problem is discretized by means of finite element method. The convergence results for the approximation are proved. The discretized versions are then formulated as a non-linear programming problem. Results of practical computations of the problem in question are reported.
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    Functional spaces for norton-hoff materials (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 206-222 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Some specific functional spaces are required for the study of Norton-Hoff materials. For this purpose we establish here a Korn's inequality and miscellaneous results of duality, traces, density and orthogonality.
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    A reaction-diffusion system modelling the spread of bacterial infections (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 234-246 
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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 a system of reaction-diffusion equations which model the spread of a bacterial infection in a human population. A decoupling technique together with global bifurcation theory is used to study the steady-state solutions of the system. The asymptotic behaviour of solutions is discussed by using sub and subersolutions and the quasimonotonicity of the system.
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    Periodic solutions of quasilinear non-autonomous systems with impulses (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 247-255 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper considers a system of differential equations with impulse perturbations at fixed moments in time of the formwhere x ∊ Rn, ε is a small parameter,Sufficient conditions have been found for existence of the periodic solution of the given system in the critical and non-critical cases.
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    A note on the nonlinear stability of a spatially symmetric vlasov-possion flow (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 284-288 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give sufficient conditions for the nonlinear stability of a, possibly non-smooth, spatially homogeneous Vlasov-Poisson flow.Research partially supported by Italian CNR and Ministero della Pubblica Istruzione.
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    A note on the solvability of Boltzmann's equation via comparison methods (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 332-339 
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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 Cauchyproblem for the space-inhomogeneous Boltzmann equation. For the so-called soft-interaction case we prove unique local solvability, analogous to a result of Palczewski [1]. However, since in our proof a comparison argument is used rather than the familiar contraction mapping principle, we are able to extend the previously known time-interval of existence. In a final section the two main difficulties in generalizing the result are discussed in some detail.
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    Optimal controllability in viscoelasticity of rate type (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 368-386 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Recently, the control engineers interest turns upon material with structural damping, such as hysteretic effects in elastoplastic systems [27] and flexible space structures [30] and in particular with damping due to the viscoelastic nature of the material, in the sense of Kelvin, [7], [12]. The reason for this renewed interest is the possibility of constructing finite rank compensators with small spillover in the observation [1], [5], [11], [25].However, a control theory for the infinite system does not seem to exist in the literature. It is shown that the trajectories, initially in a certain subspace, can be steered to rest in any time T 〉 0 using distributed load controlsThe reesults are partially contained in [19].. Furthermore, and perhaps more interesting, the L2 (0, T, H)-norm of the control decreases as T increases. This gives rise to the problem of time-optimal-controllability and the correlation to the problem of minimum norm controllability.It is shown that the time-optimal control is characterized by a weak “bang-bang” principle.
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    An algorithm for tracing the boundary curves of mushy regions in some degenerate diffusion problems (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 458-477 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We present an algorithm for approximating the solution of the degenerate diffusion problem ut = (φ(u))xx in (0,1) × R+ (with zero Dirichlet boundary conditions, and nonnegative initial datum u0), where φ(u) = min {ku1} for some ϰ 〉 0. The algorithm also provides an approximation for the interface curves which represent the boundary of the Mushy Region M = {(x, t): φ (u(x, t)) = 1}. The convergence of the algorithm is proved.
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    Evolution systems in semiconductor device modeling: A cyclic uncoupled line analysis for the gummel map (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 455-492 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The initial/boundary-value problem for isothermal, lattice, semiconductor device modeling is described and analyzed. This nonlinear elliptic/parabolic system of reaction/diffusion/convection type is determined by a Maxwell equation, relating space/charge and the electric field, and by two continuity equations for the free electron and hole carrier concentrations. The Einstein relations for Brownian motion are not assumed in this analysis, so that the electrostatic potential, u, and the carrier concentrations, n and p, are the fundamental dependent variables of the system. The boundary conditions are Dirichlet conditions for dependent variable values on the contact portions of the device, and homogeneous Neumann conditions, expressing insulation, on the complement. Complicating the analysis are the transition singularity points between the mixed boundary conditions, and the field dependence of the mobility and diffusion coefficients. By means of a physically motivated analysis of the convective current component, we are able to uncouple the system by a cyclic horizontal line analysis, without an unreasonable time step restriction. The corresponding linear equations are solved by a contractive inner iteration. The outer iteration is shown to converge to a unique solution of the system, under singularity classification at the transition points. The definition of this outer iteration follows the steady-state Gummel iteration at discrete time steps. An existence theory is a by-product of the analysis, and is separated from uniqueness theory.
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    Plane potential flow past a cylinder with porous surface (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 587-605 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the paper two models for the potential flow past a cylinder with porous or perforated surface are reduced to nonlinear Riemann-Hilbert problems for the complex velocity function and general existence and uniqueness theorems for the solution of the problems are derived. Further the problems are reduced to nonlinear singular integral equations of Hilbert type whose solvability is investigated by means of the Schauder and Banach fixed point theorem.
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    Transport equations with boundary conditions of reverse reflection type (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 15-35 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A study is performed of transport equations on arbitrary three-dimensional domains with boundary conditions of reverse reflection type. The existence of the dominant eigenvalue of the criticality problem is proved and its independence of the functional setting and its continuous dependence on a variety of data are established. The corresponding time-dependent problem is shown to be well-posed, also for a conservative boundary. The relationship between the criticality and the time-dependent problem is given explicitly.
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    Masthead (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    On the principles of limiting absorption and limit amplitude for a class of locally perturbed waveguides. Part 1: Time-independent theory (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 125-144 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let Ω be a local perturbation of the n-dimensional domain Ω0 = Ropf;n - 1 × (0, π). In a previous paper8 we have introduced the notion of an admissible standing wave. We shall prove that the principle of limiting absorption holds for the Dirichlet problem of the reduced wave equation in Ω at ω ≥ 0 if Ω does not allow admissible standing waves with frequency ω. From Reference 8, this condition is satisfied for every ω ≥ 0 if Ω ≠ Ω0, and v·x′ ≤ 0 on δΩ, where x′ = (x1,…, xn - 1, 0) and v is the normal unit vector on δΩ pointing into the complement of Ω. In contrast to this, the principle of limiting absorption is violated in the case of the unperturbed domain Ω0 at the frequencies ω = 1,2,… if n ≤ 3. The second part of our investigation, which will appear in a subsequent paper, is devoted to the principle of limit amplitude.
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    On a class of probability distributions (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 210-219 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: The application of a three parameter class of one-sided probability distributions is being discussed. For specific parameter values, this class contains as special cases a number of well-known distributions of statistics and statistical physics, namely, Gauss, Weibull, exponential, Rayleigh, Gamma, chi-square, Maxwell, and Wien (limiting case of Planck's distribution). One of the three parameters represents scale; the other two represent initial and terminal shape of the associated probability density function. A fourth parameter, shift, may be introduced. The distribution class discussed in this paper was introduced by L. Amoroso [2] in 1924. It is closely connected with a family of linear Fokker-Planck equations (generalized Feller equation). In fact, the class of probability density functions associated with the distribution class considered here is a special case of the set of all delta function initial condition solutions of the generalized Feller equation for a fixed value of the time variable. It will be shown that, as a function of the logarithm of the independent variable, the logarithm of the cumulative distribution function is asymptotically linear as the independent variable approaches zero from above. This fact leads to a general criterion for the applicability of the presented distribution family relative to given empirical data. The applicability criterion can be used to determine approximate values for the two shape parameters. They can subsequently be used as initial values in any of the established parameter estimation techniques.
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    On the construction of global weak solutions in the Kynch theory of sedimentation (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 245-264 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We construct global weak solutions to the different modes of sedimentation appearing in the theory of Kynch and show that, with constant initial concentration, only five modes of sedimentation exist. We also generalize the method of construction to the case of a monotonically decreasing initial concentration.
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    A mathematical study of a continuum-state cross-bridge model of muscle contraction (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 289-302 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the framework of the sliding-filament theory of muscle contraction, we develop a model which describes physioiogical cross-bridge activity with a continuum of states, from those which are detached and refractory to those which are attached. The latter are kinetically more important.An analytical study of the non-linear partial differential equations of the mathematical model shows existence and uniqueness of the solution.
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    Singularities of the Laplacian at corners and edges of three-dimensional domains and their treatment with finite element methods (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 339-350 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Three-dimensional Poisson problems containing boundary singularities are treated. The forms of the solutions for certain problems of this type are derived, where the domains of the problems can be represented in terms either of spherical- or of cylindrical-polar co-ordinates. These singular forms are used to augment the basis of a standard piecewise polynomial Galerkin space, thus producing an augmented Galerkin technique which is suited to the context of a problem involving a singularity. Error estimates are derived.
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    Interpolation of coefficients and transformation of the dependent variable in finite element methods for the non-linear heat equation (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 105-124 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Error estimates are shown for some spatially discrete Galerkin finite element methods for a non-linear heat equation. The approximation schemes studied are based on the introduction of the enthalpy as a new dependent variable, and also on the application of the Kirchhoff transformation and on interpolation of the non-linear coefficients into standard Lagrangian finite element spaces.
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    On the instability of resonances in parallel-plane waveguides (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 279-315 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: It has been observed13 that the propagation of acoustic waves in the region Ω0= ∝2 × (0, 1), which are generated by a time-harmonic force density with compact support, leads to logarithmic resonances at the frequencies ω = 1, 2,… As we have shown9 in the case of Dirichlet's boundary condition U = 0 on ∂Ω, the resonance at the smallest frequency ω = 1 is unstable and can be removed by a suitable small perturbation of the region. This paper contains similar instability results for all resonance frequencies ω = 1, 2,… under more restrictive assumptions on the perturbations Ω of Ω0. By using integral equation methods, we prove that absence of admissible standing waves in the sense of Reference 7 implies the validity of the principle of limit amplitude for every frequency ω ≥ 0 in the region Ω =Ω0 -B, where B is a smooth bounded domain with B̄⊂Ω0. In particular, it follows from Reference 7 in the case of Dirichlet's boundary condition that the principle of limit amplitude holds for every frequency ω ≥ 0 if n·x′ ≤ 0 on ∂ B, where x′ = (x1, x2, 0) and n is the normal unit vector pointing into the interior B of ∂ B. In the case of Neumann's boundary condition, the logarithmic resonance at ω = 0 is stable under the perturbations considered in this paper. The asymptotic behaviour of the solution for arbitary local perturbations of Ω0 will be discussed in a subsequent paper.
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    On properties of the iterative maximum likelihood reconstruction method (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 331-342 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we continue our investigations6 on the iterative maximum likelihood reconstruction method applied to a special class of integral equations of the first kind, where one of the essential assumptions is the positivity of the kernel and the given right-hand side. Equations of this type often occur in connection with the determination of density functions from measured data. There are certain relations between the directed Kullback-Leibler divergence and the iterative maximum likelihood reconstruction method some of which were already observed by other authors. Using these relations, further properties of the iterative scheme are shown and, in particular, a new short and elementary proof of convergence of the iterative method is given for the discrete case. Numerical examples have already been given in References 6. Here, an example is considered which can be worked out analytically and which demonstrates fundamental properties of the algorithm.
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    Finite element solution for the transcritical shallow-water equations (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 503-524 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new solution of the two-dimensional shallow-water equations, using a finite element method is described. The formulation is based on the velocity and height variables and follows two steps. In the first step, the convective terms are solved by a characteristic method and in the second step the propagative and diffusion terms are taken into account. The close relation between the latter operator and a Stokes penalized problem is shown; an algorithm of Uzawa type is then used for its solution. Acceleration convergence is obtained by preconditioning, and new methods are presented, the quality of the convergence being shown on application to some sample tests. The overall method has revealed quite efficient and application to industrial cases is already planned.
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    Bifurcation from the essential spectrum for some non-compact non-linearities (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 525-542 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Conditions ensuring bifurcation from the infimum of the essential spectrum are given. The main result concerns non-linear eigenvalue problems with variational structure in a Hilbert space. It extends previous results of a similar nature by admitting situations where the non-linearity is not compact with respect to the graph norm of the linearization. The general result is applied to non-linear elliptic equations on RN.
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    Stability of a smooth flow in a Laval nozzle (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 559-572 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: A boundary-value problem for a non-linear second-order equation of mixed type in a cylindrical domain is considered. This problem simulates the development of small disturbances in a transonic flow of a chemical mixture in a Laval nozzle.The existence of a regular solution is proved with the help of a priori estimates for a corresponding linear problem and the contractive mapping theorem. The solution of the linear problem is constructed by the Galerkin method.
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    On a free boundary value problem of physical geodesy, I (uniqueness)This paper is part of the author's “Habilitationsschrift”, accepted by the “Fachbereich 6 der Universität - Gesamthochschule - Essen”. (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 269-289 
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    Notes: The determination of the figure of the earth is considered as a local free boundary value problem of potential theory: the shape of a slowly rotating heavy body has to be found from the boundary data of the attracting force and its potential outside of the body, provided that an approximation to the solution is already known. In this paper a uniqueness result is proved which is local with respect to the C1-topology.
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    Feynman-diagramme als vektorsysteme invariantentheoretisch behandelt (compton-streuung, elektron-positron-vernichtungDiese Arbeit wurde aus Mitteln der Deutschen Forschungsgemeinschaft gefördert. (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 309-330 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Employing a special contact transformation devised by S. Lie, which takes spheres into lines, we interpret the Feynman diagrams of photon electron scattering in terms of vector systems. This gives a nice kinematic model of Compton scattering. We further compute in detail the transition probabilities of the Compton scattering process by making use of the calculus of chains of complexes from classical invariant theory rather than applying the usual Dirac-matrix technique. In the final paragraph of this paper an application of our calculations to the treatment of myon decay is indicated.
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    On the existence of optimum large amplitude hydrofoil propulsion II (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 346-366 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The possibility of optimum thrust-production by means of a flexible profile is discussed using a linearized theory. By applying the theory of trace theorems and Rellich's lemma, it is shown that there exists an optimum path for the profile in every class which consists of paths having uniformly bounded amplitudes and slopes.
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    Taylor series for the dirac function on perturbed surfaces with applications to mechanics (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 416-425 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Let H0 be the Hamiltonian of an unperturbed oscillating system and let V be a small perturbation which is analytic in a neighborhood of the surface H0 = E, E 〉 0.If H0 = H + λ V is the total Hamiltonian, we prove that there is a Taylor expansion of the Dirac function δ for small |λ|When applied to test functions which are analytic near H0 = E.The connection of this result with the classical Lagrange-Bürmann theorem and some applications to the mechanics of non-linear systems are discussed.
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    A class of explicitly resolvable evolution equations (1985)
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    Mathematical Methods in the Applied Sciences 7 (1985), S. 426-431 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a class of evolution equations with “scalar nonlinearities” and the associated steady equations. An explicit representation of solutions is obtained in terms of the solution of a scalar nonlinear functional differential equation. Convergence to an equilibrium solution is discussed.
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    Examples involving the geometric form of level curves of harmonic functions (1985)
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    Mathematical Methods in the Applied Sciences 7 (1985), S. 480-485 
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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 x-y plane, we give, for example, a Jordan curve Γ containing exactly one local maximum and one local minimum in the y-direction, such that some level curve of the capacity potential in the exterior complement of Γ has at least n local maxima and n local minima in the y-direction, n being any prescribed number.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670070134
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    A remark on N. Korevaar's concavity maximum principle and on the asymptotic uniqueness of solutions to the plasma problem (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 93-101 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently N. Korevaar developed a method of proving that solutions to elliptic and parabolic boundary value problems on convex domains ω ⊂ Rn are convex functions. He introduced a concavity functionand used the classical maximum principle to prove that C ≥ 0 on ω × ω, i.e. that u is convex. Both he and independently L. Caffarelli and J. Spruck applied this method successfully to various boundary value problems. In this note we weaken the assumptions of their theorems and obtain some interesting new applications which are not covered by their previous results [CS, Ko].
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    URL: http://dx.doi.org/10.1002/mma.1670080107
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    Distribution of resistive body-force in curved free-surface flow (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 492-501 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The customary procedure for including resistive effects in turbulent hydraulic and stratified atmospheric flows is to integrate the empirically-known boundary shears over the entire wetted boundary of a thin fluid slab. A resistive body-force is then assumed to exist everywhere in each slab to replace the boundary shearing force. For the classical Saint-Venant model, this body-force can be shown to have a constant distribution in the vertical direction, and therefore can be evaluated for use in the momentum differential equation. In the newer Dressler theory, however, for unsteady flow over curved beds, it is proved here that a constant body-force distribution is not possible. We determine its variable distribution and its magnitude for use in the curved-flow equations. This vasriable distribution acts to produce an equal resultant in every thin layer of fluid parallel to the bed in an angular wedge over the curved channel bed. The new curved-flow equations are therefore extended to include resistive effects.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670080132
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    On the simulation source technique for exterior problems in acousticsThis research was carried out while the second author was visiting the University of Göttingen on a Humboldt stipendium. (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 585-597 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For the solution of the exterior Dirichlet problem for the Helmholtz equation we propose to seek the solution in the form of an acoustic single-layer potential with a distribution extended over an internal surface. This leads to an ill-posed integral equation of the first kind which can be approximately solved by the Tikhonov regularization technique.
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    URL: http://dx.doi.org/10.1002/mma.1670080138
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    Formulation variationnelle pour le calcul de la diffraction d'une onde acoustique par une surface rigide (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 598-608 
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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 a continuation of [1]. We give a space-time variational formula to the problem of the scattered acoutic wave by a hard body, using the double layer retarded potential technique. New schemes are constructed from this variationnal formula, for which we prove the stability and errors estimates.
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    URL: http://dx.doi.org/10.1002/mma.1670080139
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    Some algorithms of the projective-Newton method for the finite element space (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 1-12 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper presents the projective-Newton method in the finite element space with curved finite elements along the boundary. The properties of this method are studied when the integrals are calculated by numerical quadrature. Some algorithms are derived when ω = {x ∊ R2: 0 〈 x1, x2 〈 1}.
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    URL: http://dx.doi.org/10.1002/mma.1670090102
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    High velocity particles in a collisionless plasma (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 46-52 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove that smooth solutions of the relativistic Vlasov-Maxwell equations exist for all time provided the kinetic energy density is uniformly bounded.
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    URL: http://dx.doi.org/10.1002/mma.1670090105
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    Motion of a vibrating string in the presence of a convex obstacle: A free boundary problem (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 276-297 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Here we study the motion of a vibrating string in the presence of an arbitrary obstacle. We show that if the string always rebounds on the concave parts of the obstacle, it can either rebound or roll on the convex parts. The latter is the case if the velocity of the string is null at the contact point just before contact, or if the contact point propagates at a characteristic speed. Four examples are given. The three first correspond to the same obstacle, a sinusoidal arc, but with different initial conditions. In the first case, the string rebounds on the whole of the obstacle and the motion is explicitly determined when it is periodic. In the second case, the string rolls on the convex part of the obstacle up to the inflexion point and then rebounds on the concave part and unwinds on the convex part. In the third case, the string is initially at rest on the obstacle; then it instantaneously leaves the concave part while it unwinds progressively on the convex part. The fourth case is similar to the third but with a different obstacle; the motion, which is periodic, is determined explicitly.
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    URL: http://dx.doi.org/10.1002/mma.1670090122
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    On approximation to convective diffusion equation (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 399-412 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A closed-form analytical solution for the problem of homogeneous and heterogeneous reactions in a isothermal non-Newtonian laminar flow tubular reactor is presented. A technique is evolved where Galerkin method is applied in Laplace-transformed domain.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670090129
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    A free boundary problem for three-dimensional harmonic vector fields (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 367-398 
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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 in this paper a free boundary value problem (FB), where a region Go in R3 is determined by the condition that there exists a vector field vo in Go which satisfies div vo = eo, curl vo = go in Go and vo = E on the boundary ∂Go with a given scalar function eo and given vector fields go and E. We give two equivalent formulations for this problem. Then we characterize the solutions by a non-linear integral equation. In order to solve the latter by a Newton method we linearize this equation. We investigate the ensuing linear integral equation. In case of axisymmetric configurations this is a singular integral equation whose index can be easily determined from the given data. We obtain a related equation, if we try to construct a field v in a region G which is on the boundary perpendicular to a given field B. Finally we use this method to investigate an astrophysical problem, which arises in the theory of pulsar magnetospheres.
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    URL: http://dx.doi.org/10.1002/mma.1670090128
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    The Galerkin-averaging method for nonlinear, undamped continuous systems (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 520-549 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The analysis of initial-boundary value problems for nonlinear evolution equations with a small parameter is carried out by projection and averaging. The complications of the extension to a second order approximation is discussed and subsequently demonstrated for the perturbed Klein-Gordon equation. The difference between the case of resonance and nonresonance at first order is emphasized.
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    URL: http://dx.doi.org/10.1002/mma.1670090134
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    Über das homogene Dirichlet-Problem bei nichtlinearen partiellen Differentialgleichungen vom Typ der Boussinesq-Gleichung (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 493-519 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Semilinear equations of Boussinesq type, e.g. utt + uxx - uxxxx + (u2)xx = 0, utt + uxx - uxxxx + uxuxx = 0, or certain equations containing the squared wave operator, e.g. uxxtt - uk = 0, k ∊ N k ≥ 2, are studied. A generalized boundary value problem on bounded domains can be treated using Hilbert space methods. The linear parts of these equations are not elliptic, the latter not even hypoelliptic. A mountain pass lemma is used to prove the existence of nontrivial weak solutions. These solutions are obtained in anisotropic Sobolev spaces.
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    URL: http://dx.doi.org/10.1002/mma.1670090133
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    Weak travelling fronts for population models with density dependent dispersion (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 576-586 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670090136
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    Approximation dans un Problème de Viscoélasticité PériodiqueCe travail a été effectué durant le séjour de l'auteur, en tant qu'associé, au laboratoire d'Analyse numérique et Mécanique de l'Université de Rennes I. (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 606-626 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We are concerned with equations which derive from a quasistatic periodic problem of viscoelasticity. We give a condition which yields to existence and uniqueness of a periodic solution. Then we prove a finite element method based on equilibrium elements for the space approximation and on the explicit Euler scheme for the time approximation.
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    URL: http://dx.doi.org/10.1002/mma.1670090138
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    Non-linear boundary value problems for the annular membrane: New results on existence of positive solutionsDedicated to Professor Wolfgang Wendland on the occasion of his 50th anniversary (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 37-49 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Föppl-Hencky theory of small finite deflections has been applied to the study of axisymmetric deformations of annular membranes by various authors. The mathematical problem of uniqueness of tensile solutions for the corresponding non-linear boundary value problems in the full range of physically meaningful boundary data was solved only recently.3, 4 In this paper, a new integral equation technique of solution is developed which yields the existence of tensile solutions for a parameter range of the boundary data where previous investigations on this matter had not been successful. It is shown that tensile solutions no longer exist, when sufficiently large positive radial displacements are prescribed at the inner edge of the annulus.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670100104
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    On a thermal stress problem for contacting half-spaces with inclusions of other material involving a new method for computing potentials and singular integrals (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 225-243 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with a thermal stress problem for contacting half-spaces of different materials having an inclusion of other material. With the aid of the contact tensor of two half spaces the problem is reduced to singular integral equations. Some new theorems on potentials with the contact tensor are used. Finally, a potential of the double layer with the contact tensor in the kernel and a singular integral operator, being the direct value of the potential, are calculated. For this a Kupradze method is applied, interpreting this potential as a solution of a contact problem of elastostatics. Some numerical experiments are communicated.
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    URL: http://dx.doi.org/10.1002/mma.1670100303
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    On the stationary flows of viscous, incompressible and heat-conducting fluids (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 329-337 
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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 a boundary-value problem describing the motion of viscous, incompressible and heat-conducting fluids in a bounded domain in ∝3. We admit non-homogeneous boundary conditions, the appearance of exterior forces and heat sources.Our aim is to prove the existence of a solution of the problem in Sobolev spaces.
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    URL: http://dx.doi.org/10.1002/mma.1670100308
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    Inversion of the exponential X-ray transform. I: Analysis (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 561-574 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The exponential X-ray transform arises in single photon emission computed tomography and is defined on functions on ∝n by , where μ is a constant. Approximate inversion, and inversion formulae of filtered back-projection type are derived for this operator in all dimensions. In particular, explicit formulae are given for convolution kernels (filters) K corresponding to a general point spread function E that can be used to invert the exponential X-ray transform via a filtered back-projection algorithm. The results extend and refine work of Tretiak and Metz17.
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    URL: http://dx.doi.org/10.1002/mma.1670100506
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    Injection of ideal fluid from two slots into a stream (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 585-594 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A cold gas is injected from two slots into a stream of hot gas. In a simple model this leads to a three-phase two-free-boundary problem. We prove, using the variational theory of Alt, Caffarelli and Friedman, the existence of the classical solution.
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    URL: http://dx.doi.org/10.1002/mma.1670100508
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