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  • Mathematics and Statistics
  • Wiley-Blackwell  (603)
  • Blackwell Publishing Ltd
  • 1995-1999  (263)
  • 1985-1989  (340)
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Publisher
  • Wiley-Blackwell  (603)
  • Blackwell Publishing Ltd
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Year
  • 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
    Electronic Resource
    Electronic Resource
    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
    Electronic Resource
    Electronic Resource
    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
    Electronic Resource
    Electronic Resource
    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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    Electronic Resource
    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
    Electronic Resource
    Electronic Resource
    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
    Electronic Resource
    Electronic Resource
    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
    Electronic Resource
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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 
    Details
    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 
    Details
    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
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    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.
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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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    Keywords: Mathematics and Statistics ; Applied Mathematics
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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
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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
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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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    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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    Vacuum and non-vacuum solutions of the quasi-hydrodynamic semiconductor model in thermal equilibrium (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 225-254 
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    Notes: The quasi-hydrodynamical model for bipolar semiconductor devices in thermal equilibrium admits in general solutions for which the non-negative electron- or hole-density is not strict positive. In this paper sufficient conditions depending on the device's data which lead to or prevent vacuum are presented. The transformation of the model equations to a single semilinear elliptic mixed boundary value problem for the electrostatic potential V reduces the vacuum-non-vacuum discussion to an investigation of the range of V. Monotonicity arguments and the employment of local sub- and supersolutions allow to estimate the size as well as the distance from the Dirichlet boundary of the respective vacuum sets. An one-dimensional model is analysed in some detail.
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    Global existence and blow-up for a system of heat equations with non-linear boundary conditions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 307-315 
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    Notes: In this paper, we consider non-negative solutions of We prove that if pq ≤ 1 every solution remains bounded, while all solutions blow up in a finite time if pq 〉 1. We also show that if p,q 〉 1, then blow-up can only occur on the boundary.
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    On the sharp singular limit for slightly compressible fluids (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 295-306 
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    Notes: We consider the equations of motion to slightly compressible fluids and we prove that solutions converge, in the strong norm, to the solution of the equations of motion of incompressible fluids, as the Mach number goes to zero. From a physical point of view this means the following. Assume that we are dealing with a well-specified fluid, so slightly compressible that we assume it to be incompressible. Our result means that the distance between the (continuous) trajectories of the real and of the idealized solution is ‘small’ with respect to the natural metric, i.e. the metric that endows the data space.
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    Boundary layer resolution in hierarchical plate modelling (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 345-370 
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    Notes: The dimensional reduction of an elliptic model boundary value problem on a thin, plate-like domain of thickness 2d is analysed. A class of lower-dimensional models with variable model orders in the interior and near the boundary of the plate is investigated and it is shown that for a sufficiently large model order in a O(d∣ln d∣)-neighbourhood of the edge the hierarchical models compensate for the boundary layers of the exact solution - in the sense that their asymptotic rate of convergence as d → 0 is the same as the optimal one for compatible, layer-free solutions.
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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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    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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    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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    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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    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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    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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    Similarity solutions of dispersive long-wave equations in two space dimensions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 789-802 
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    Notes: In this paper, both the direct method and the non-classical Lie approach are applied to reduce the (2 + 1)-dimensional dispersive long wave equations. Nine types of two-dimensional PDE reductions and 13 types of ODE reductions are given. All the known reductions obtained by the classical Lie approach are reobtained as some special cases. Similar to the (1 + 1)-dimensional case, some types of reductions with essential and logarithmic singular characteristic manifolds are allowed although the model is integrable.
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    On the initial value problem for the Vlasov-Poisson-Fokker-Planck system with initial data in Lp spaces (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 825-839 
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    Notes: In this paper the global existence of weak solutions for the Vlasov-Poisson-Fokker-Planck equations in three dimensions is proved with an L1 ∩ Lp initial data. Also, the global existence of weak solutions in four dimensions with small initial data is studied. A convergence of the solutions is obtained to those built by E. Horst and R. Hunze when the Fokker-Planck term vanishes. In order to obtain the a priori necessary estimates a sequence of approximate problems is introduced. This sequence is obtained starting from a non-linear regulation of the problem together with a linearization via a time retarded mollification of the non-linear term. The a priori bounds are reached by means of the control of the kinetic energy in the approximate sequence of problems. Then, the proof is completed obtaining the equicontinuity properties which allow to pass to the limit.
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    An explicit solution of the pseudo-hyperbolic initial boundary value problem in a multiply connected region (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 897-925 
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    Notes: An explicit solution of the pseudo-hyperbolic initial boundary value problem with a mixed boundary condition has been constructed. The problem describes the propagation of non-stationary internal waves in a stratified and rotational fluid. The generation of waves is caused by small oscillations of double-sided plates beginning at time t = 0. Dynamic pressure is specified on one set of plates and this yields the first boundary condition. Normal velocities are specified on another set of plates and this leads to an analogue of the second boundary condition with time derivatives. The solution has been obtained by the method of non-classical time-dependent dynamic potentials. The uniqueness of the solution has been studied.
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    A discrete velocity coagulation-fragmentation model (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 959-993 
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    Notes: A discrete velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in a volume V with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker-Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. Results of numerical experiments are presented.
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    On a local in time solvability of the Neumann problem of quasilinear hyperbolic parabolic coupled systems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1053-1082 
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    Notes: We prove a local in time existence theorem of classical solutions to some coupled system of quasilinear hyperbolic equations and quasilinear parabolic equations with Neumann boundary condition. This coupled system contains a non-linear thermoelastic equation as an important physical example.
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    On the one- and one-half-dimensional relativistic Vlasov-Fokker-Planck-Maxwell system (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1013-1040 
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    Notes: In this paper, we study the relativistic Vlasov-Fokker-Planck-Maxwell system in one space variable and two momentum variables. This non-linear system of equations consists of a transport equation for the phase space distribution function combined with Maxwell's equations for the electric and magnetic fields. It is important in modelling distribution of charged particles in the kinetic theory of plasma. We prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique.
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    A particle method for a self-gravitating fluid: A convergence result (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1083-1094 
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    Notes: We study an Hamiltonian system of N particles in ∝3 interacting by a short-range repulsive and a long-range attractive potential. It is shown that the empirical measures associated to the positions and velocity of the system converge to the solutions of Euler equations for a self-gravitating fluid, in the limit as the particle number tends to infinity, for a suitable scaling of the interactions.
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    Periodic optimal control for parabolic Volterra-Lotka type equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 127-146 
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    Notes: This paper considers the optimal harvesting control of a biological species, whose growth is governed by the parabolic diffusive Volterra-Lotka equation. We prove that such equation with L∞ periodic coefficients has an unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions, we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed.
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    Asymptotic characterization of standing waves and of the static limit for a class of wave equations of higher order with a variable coefficient and time-independent incitation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 147-168 
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    Notes: We consider the equation (-1)m∇m (p∇mu) + ∂t2u = ƒ in ∝n × (0, ∞) for arbitrary positive integers m and n and under the assumptions p - 1, ƒ ∊ C0∞(∝n) and p 〉 0. Even if the differential operator (-1)m∇m (p∇mu) has no eigenvalues, the solution u(x,t) may increase as t → ∞ for 2m ≥ n. For this case, we derive necessary and sufficient conditions for the convergence of u(x,t) as t → ∞. Furthermore, we characterize the functions occurring in these conditions as solutions of the homogeneous static equation (-1)m∇m (p∇mu) = 0, which satisfy appropriate asymptotic conditions at infinity. We also give an asymptotic characterization of the static limit.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Existence of a solution for a lubrication problem in elastic journal-bearing devices with thin bearing (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 255-266 
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    Notes: A particular elastohydrodynamic lubrication problem is modelled in this work. The presence of elasticity, lubrication and cavitation calls for a non-linear coupled system of variational equations. The existence of a solution is deduced by means of a constructive algorithm that decouples biharmonic equation of the elastic hinged plate and the lubrication-cavitation Elrod-Adams free boundary problem.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    On the bending of plates with transverse shear deformation and mixed periodic boundary conditions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 337-344 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The method of matched asymptotic expansions is used to find a homogenized problem whose solution is an approximation to the solution of a mixed periodic boundary value problem in the theory of bending of thin elastic plates. A critical size for the fixed parts of the boundary is found such that the boundary condition of the homogenized problem is an intermediate case between that for the clamped edge plate and that for the free boundary plate.
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    The free boundary problem of a semiconductor in thermal equilibrium (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 387-412 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The quasi-hydrodynamic model for semiconductor devices in thermal equilibrium admits in general solutions for which the electron or hole density vanish. These sets are called vacuum sets. In this paper estimates on the vacuum sets and a first step in the regularity of the free boundary of these sets are presented. Numerical examples, including error estimates for linear finite elements, for the devices diode, bipolar transistor and thyristor indicate that the free boundary is more regular than theoretically predicted.
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    Thermal deformations of inhomogeneous elastic plates (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 423-436 
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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 thermal deformations of transversally inhomogenous elastic plates. Thin plate equations are derived as limits of full three-dimensional models both in the linear as well as in the non-linear case with appropriate convergence proofs. In the non-linear case also the corresponding von Kármán equations are formulated. It is obtained that the inhomogeneity leads to the loss of some symmetry properties at the von Kármán equations.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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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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    The double layer potential method for a boundary transmission problem for the Laplace operator in an infinite wedge (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 515-528 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the solution of a boundary transmission problem in an infinite wedge. We treat this problem by a boundary integral method using Green's contact function for two half-spaces. The integral operators are studied via a harmonic analysis approach which goes back to a paper of Fabes et al. We improve their results studying the Fourier symbol of the associated integral operators on the half-plane. This leads to invertibility criteria for the boundary integral operators.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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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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    About the concept of measure-valued solutions to distributed parameter systems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 671-685 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The measure-valued (mv) solutions are commonly defined in the literature simply by putting Young measures into the respective partial differential equations. Here a few examples of mv-solutions to evolution problems (conservation laws, fluid dynamics and a so-called backward-forward heat problem) are re-investigated to show that such definitions are not satisfactorily selective, i.e. they admit (sometimes surprisingly) many mv-solutions apparently without any physical sense. Then an attempt for a selective definition in the case of the backward-forward heat problem is made, resulting to a certain evolution variational inequality.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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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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    A new system of boundary integral equations for plates with free edges (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 755-772 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a new system of boundary integral equations for the free-edge plate. This system expresses an abstract symmetric variational problem posed on the boundary of the plate. In order to obtain this abstract problem, we must set the exterior boundary value problem corresponding to the free-edge plate in a framework of weighted Sobolev spaces. Finally, we take care of the hypersingular kernels appearing in our system of BIEs, by using an abstract technique of integration by parts.
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    The sorption of mixtures under linear equilibrium partitioning and chemical transformation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 803-823 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the flow of a mixture, whose components are undergoing temporally and spatially varying linear equilibrium sorption partitioning and, possibly nonlinear, chemical transformations. We are able to generate an evolution system of parabolic type on the space of uniformly continuous functions and thus obtain classical solutions for arbitrary initial values.
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    Large time asymptotics for a class of wave equations of higher order with a variable coefficient and time-independent incitation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1-25 
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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 equation (-1)m∇m (p∇mu) + ∂t2u = ƒ in ∝n × [0, ∞] for arbitrary positive integers m and n and under the assumptions p -1, ƒ ∊ C0∞ and p 〉 0. Under the additional assumption that the differential operator (-1)m∇m (p∇mu) has no eigenvalues we derive an asymptotic expansion for u(x,t) as t → including all terms up to order o(1). In particular, we show that for 2m ≥ n terms of the orders tα, log t, (log t)2 and tβ·log t as t → ∞ may occur.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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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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    Non-orthogonal expansions on the sphere (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 83-120 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Discrete families of functions with the property that every function in a certain space can be represented by its formal Fourier series expansion are developed on the sphere. A Fourier-series-type expansion is obviously true if the family is an orthonormal basis of a Hilbert space, but it also can hold in situations where the family is not orthogonal and is ‘overcomplete’. Furthermore, all functions in our approach are axisymmetric (depending only on the spherical distance) so that they can be used adequately in (rotation) invariant pseudo-differential equations on the sphere. The three classes of examples particularly studied here are (i) Abel-Poisson frames (ii) Gauss-Weierstrass frames and (iii) frames consisting of locally supported kernel functions. Abel-Poisson frames form families of harmonic functions and provide us with powerful approximation tools in potential theory. Gauss-Weierstrass frames are intimately related to the diffusion equation on the sphere and play an important role in multiscale descriptions of image processing on the sphere. The third class enables us to discuss spherical ‘Fourier expansions’ by means of ‘axisymmetric finite elements’.
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    Local existence of solutions of impedance initial-boundary value problem for non-linear Maxwell equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 169-199 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Local existence of solutions of a mixed problem for non-linear Maxwell equations is proved. The solution is so regular that its third derivatives are from L2. However, the considered problem is characteristic we were able to obtain necessary estimate because compatibility conditions were used.
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    Inverse scattering from an open arc (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 267-293 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound-soft or perfectly conducting arc from a knowledge of the far-field pattern for the scattering of time-harmonic plane waves. Fréchet differentiability with respect to the boundary is shown for the far-field operator, which for a fixed incident wave maps the boundary arc onto the far-field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.
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    Global solutions for operator Riccati equations with unbounded coefficients: A non-linear semigroup approach (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 317-336 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Let X be a Banach space of real-valued functions on [0, 1] and let ℒ(X) be the space of bounded linear operators on X. We are interested in solutions R:(0, ∞) → ℒ(X) for the operator Riccati equation \documentclass{article}\pagestyle{empty}\begin{document}$$ R′ + TR + RT = TB_1 (t) + TB_2 (t)R + RTB_3 (t) + RTB_4 (t)R, $$\end{document} where T is an unbounded multiplication operator in X and the Bi(t)'s are bounded linear integral operators on X. This equation arises in transport theory as the result of an invariant embedding of the Boltzmann equation. Solutions which are of physical interest are those that take on values in the space of bounded linear operators on L1(0, 1). Conditions on X, R(0), T, and the coefficients are found such that the theory of non-linear semigroups may be used to prove global existence of strong solutions in ℒ(X) that also satisfy R(t) ∊ ℒ(L1(0,1)) for all t ≥ 0.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Remark on a trace theorem for transmission problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 413-421 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we discuss elliptic transmission problems of second order in plane non-smooth domains with non-homogeneous boundary data. It is known that if the boundary data are homogeneous, then the variational solution of the transmission problem admits a representation as a sum of a regular function and certain singular functions, analogous to that encountered in boundary value problems on corner domains. We determine for which domains arbitrary non-homogeneous boundary data can be reduced to the homogeneous ones preserving availability of the representation formula. In the remaining cases we find the compatibility conditions for the data which also yield such a reduction.
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    Averaging in non-linear advective transport problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 437-448 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Advective transport in a tidal basin is modelled by a non-linear parabolic equation with initial-boundary values. The model includes small effects such as diffusion, the reststream, reaction effects and sources. For a given periodic flow field, the long-time behaviour of the solutions is approximated by using the averaging method. We show the existence of a periodic solution and we demonstrate the asymptotic validity of the approximations for all time using maximum principles.
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    A generalization of the H-theorem to steady non-equilibrium states. Part 1: A basic decomposition and the linear case (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 507-513 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: A generalized relative entropy functional is associated to the evolution of gas in a container with (generally) non-uniform boundary data. A decomposition for its rate in ‘bulk’ and in ‘boundary’ terms is given; for the linear case both have a definite sign. The relation with the strong L1 stability is pointed out.
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    Stability of semilinear ill-posed problems with a prescribed energy bound (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 549-569 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In the present paper we discuss the stability of semilinear problems of the form Aαu + Gα(u) = ƒ under assumption of an a priori bound for an energy functional Eα(u) ≤ E, where α is a parameter in a metric space M. Following [11] the problem Aαu + Gα(u) = ƒ, Eα(u) ≤ E is called stable in a Hilbert space H at a point α ∊ M if for any ƒ∊H, E, ∊ 〉 0 there exists δ 〉 0 such that for any functions uα1, uα2 satisfying Aαjuαj + Gαj(uαj) = ƒαj, Eαj(uαj) ≤ E, j = 1,2 we have ‖uα1 - uα2H ≤ ∊ provided ρM(αj, α) ≤ δ, ‖ƒαj - ƒ‖H ≤ δ, j = 1,2. In the present paper we obtain stability conditions for the problem Aαu + Gα(u) = ƒ, Eα(u) ≤ E.
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    Convergence of alternating domain decomposition schemes for kinetic and aerodynamic equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 649-670 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: A domain decomposition scheme linking linearized kinetic and aerodynamic equations is considered. Convergence of the alternating scheme is shown. Moreover the physical correctness of the obtained coupled solutions is discussed.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Quaternionic representation of the 3D elastic and thermoelastic boundary problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 697-708 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: This paper contains new representations of the 3D elasticity and thermoelasticity problems, expressed in terms of regular quaternion functions, which in 3D and 4D have properties analogous to those of complex analytical functions in 2D. The known and some new results, described in the paper, are used to formulate boundary 3D problems, related to the theory. The formulae obtained are very similar to those given by Muskhelishvili for 2D boundary problems. The obtained representations can be used for development of a 3D boundary element method in numerical analysis.
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    Calculation of microstrains and microstresses in a thick non-symmetric heterogeneous plate by homogenization (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 723-737 
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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 thermoelastic behaviour of a thick heterogeneous plate containing in its thickness a large number of periodically distributed transverse holes or inclusions. We use the Reissner-Mindlin thermoelastic linear model of thick plates with a known temperature and we distinguish displacements in the upper and lower part of the plate with respect to the middle plane. Due to the structure of the plate, thermal and elastic coefficients are non-uniformly and rapidly oscillating functions of the space variable. Two-scale convergence, which is the state of the art in mathematical homogenization technics, is used and gives convergence results and formulae allowing to calculate the distribution of microstrains and microstresses inside the plate when a macroscopic behaviour is given.
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    Global wellposedness for quasi-linear symmetric hyperbolic systems with regularized coefficients (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 773-787 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Following the abstract setting of [8] and using the global results of [2], global wellposedness and regularity results are proved for the solutions of quasi-linear symmetric hyperbolic systems with bounded coefficients which are regularized by a convolution in the space variables with a regularizing function. In the case of unbounded regularized coefficients, local existence of classical solutions is proved, as well as uniqueness and regularity of (not necessarily existing) global weak solutions with initial value in a Sobolev space. As the regularizing function tends to Dirac's δ, local-in-time convergence to the classical solution of the non-regularized problem is proved.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    On the stationary quasi-Newtonian flow obeying a power-law (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 927-948 
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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 in this paper existence of a weak solution for a stationary incompressible Navier-Stokes system with non-linear viscosity and with non-homogeneous boundary conditions for velocity on the boundary. Our concern is with the viscosity obeying the power-law dependence ν(ξ) = ∣Tr(ξξ*)∣r/2-1, r 〈 2, on shear stress ξ. It is corresponding to most quasi-Newtonian flows with injection on the boundary. Since for r ≤ 2 the inertial term precludes any a priori estimate in general, we suppose the Reynolds number is not too large. Using the specific algebraic structure of the Navier-Stokes system we prove existence of at least one approximate solution. The constructed approximate solution turns out to be uniformly bounded in W1,r (Omega;)n and using monotonicity and compactness we successfully pass to the limit for r ≥ 3n/(n + 2). For 3n/(n + 2) 〉 r 〉 2n/(n + 2) our construction gives existence of at least one very weak solution. Furthermore, for r ≥ 3n/(n + 2) we prove that all weak solutions lying in the ball in W01,r of radius smaller than critical are equal. Finally, we obtain an existence result for the flow through a thin slab.
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    On some second-order non-linear systems of a hyperbolic-parabolic type (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 949-957 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider local solutions to the Cauchy problem for a class of non-linear hyperbolic-parabolic systems generalizing the systems of elasticity and thermoelasticity. Our main purpose is to relax the usual regularity requirements to include the nonclassical solutions into considerations.
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    Masthead (1995)
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    Mathematical Methods in the Applied Sciences 18 (1995) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    The free streaming operator: A mathematical model for diffusive multiplying boundary conditions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1165-1180 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show that the free streaming operator with diffusive multiplying boundary conditions is the generator of a quasi-bounded semigroup. We also examine some spectral properties of such an operator.
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    URL: http://dx.doi.org/10.1002/mma.1670181404
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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 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670070102
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670070105
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Additional Material: 2 Tab.
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    URL: http://dx.doi.org/10.1002/mma.1670070108
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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 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670070111
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670070114
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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 (*).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070117
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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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    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.1670070121
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670070125
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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 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670070127
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670070130
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670070132
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    Masthead (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080101
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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 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670080102
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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 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670080105
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