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  • Mathematics and Statistics  (240)
  • Wiley-Blackwell  (240)
  • Annual Reviews
  • 2005-2009
  • 1990-1994  (240)
  • 1980-1984
  • 1994  (133)
  • 1993  (107)
Collection
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  • Wiley-Blackwell  (240)
  • Annual Reviews
Years
  • 2005-2009
  • 1990-1994  (240)
  • 1980-1984
Year
  • 1
    Electronic Resource
    Electronic Resource
    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    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.1670160101
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  • 2
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    Behaviour of mushy regions under the action of a volumetric heat source (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 35-47 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider solutions to Stefan problems in spatial dimensions N ≥ 1. We find the necessary conditions on the heat source for the appearance of a ‘mushy region’ (i.e. a region where the temperature coincides identically with the temperature of the change of phase) inside a purely liquid (or solid) phase. For sources depending on energy such conditions are connected only with the local behaviour of the source near the energy level corresponding to the beginning of the change or phase. Both weak and smooth solutions are considered; in the latter case the behaviour of the solution at the free boundary is investigated in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160104
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  • 3
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    On the asymptotic growth of the solutions of the vlasov-poisson system (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 75-85 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show the global existence of classical solutions of the Vlasov-Poisson system and improve the known growth estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160202
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  • 4
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    High-frequency asymptotics in inverse scattering by ellipsoids (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 1-12 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A triaxial ellipsoid of unknown position, size and orientation is located somewhere in space. High-frequency asymptotics for the scattering amplitude and the sojourn time for the travelling of a high-frequency acoustic plane wave are utilized to determine the position of a supporting plane for the ellipsoid. We describe a method that identifies the coordinates of the centre, the three semiaxes, and the three angles of the ellipsoid from the knowledge of nine sojourn times corresponding to nine directions of excitation. The method is independent of boundary conditions, it is applicable to any restricted non-zero-measure angle of observation, and leads to numerics that avoid elliptic integrals. A priori information about the location of the ellipsoid reduces the number of measurements to six, while the corresponding algorithm demands the solution of a linear system and the inversion of a dyadic.
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    URL: http://dx.doi.org/10.1002/mma.1670160102
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  • 5
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    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.1670160201
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  • 6
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    Schauder estimates for boundary layer potentials (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 877-894 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Boundary layer potentials with Hölder-continuous densities are widely used for representing solutions of boundary value problems for certain partial differential equations. These potentials are of the type with |ρ| odd and a density λ of class Ck+α. This paper presents a self-contained exposition of the fact that the potential v may be continued as Ck+α-functions onto G and ∝n\G respectively (together with estimates for the Hölder-norms) under the least possible regularity assumption for the boundary ∂G: it has to be of class Ck+1+α.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161204
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  • 7
    Electronic Resource
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    Beyond quenching for singular reaction-diffusion problems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1-9 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let f(u) be twice continuously differentiable on [0, c]) for some constant c such that f(0) 〉 0,f′ ≥ 0,f″ ≥ 0, and limu→cf(u) = ∞. Also, let χ(S) be the characteristic function of the set S. This article studies all solutions u with non-negative ut, in the region where u 〈 c and with continuous ux for the problem: uxx - ut = - f(u)χ({u 〈 c}), 0 〈 x 〈 a, 0 〈 t 〈 ∞, subject to zero initial and first boundary conditions. For any length a larger than the critical length, it is shown that if ∫0cf(u) du 〈 ∞, then as t tends to infinity, all solutions tend to the unique steady-state profile U(x), which can be computed by a derived formula; furthermore, increasing the length a increases the interval where U(x) ≡ c by the same amount. For illustration, examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170102
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  • 8
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    Approximating sequences for heteroclinic orbits (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 71-76 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we construct two approximating sequences for heteroclinic solution to a scalar ODE. These sequences do not ‘intersect’ and bound a unique real solution from below and above, thus enabling us to estimate this solution with any accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170106
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  • 9
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    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    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.1670170201
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  • 10
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    The existence of solutions of a general boundary value problem for the divergence (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 95-105 
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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 question of necessary and sufficient conditions to find a vector field V∊ Γ(TM) solving the equation div V = Φ under inhomogeneous boundary conditions V|∂M = Z|∂M with Z∊ Γ (TM) An existence and regularity result is given for an arbitrary Riemannian manifold with boundary, M. The proof is based on the Hodge theory of differential forms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170203
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  • 11
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    Local compactness for linear elasticity in irregular domains (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 107-113 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For the theory of boundary value problems in linear elasticity, it is of crucial importance that the space of vector-valued L2-functions whose symmetrized Jacobians are square-integrable should be compactly embedded in L2. For regions with the cone property this is usually achieved by combining Korn's inequalities and Rellich's selection theorem. We shall show that in a class of less regular regions Korn's second inequality fails whereas the desired compact embedding still holds true.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170204
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  • 12
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    Mathematical problems of liquid crystal flows (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 171-188 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article deals with flow phenomena in liquid crystal materials. The model that I analyse is that due to Ericksen for liquid crystals with variable degree of orientation. One of the goals is understanding the role of the order parameter in the model. I examine the multiplicity of solutions, phases, that occur in shear flow regimes and analyse their stability under physically realistic conditions. In particular, I show that ellipticity of the linearized system of governing equations is a consequence of the Clausius-Duhem inequality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170303
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  • 13
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    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    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.1670170401
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  • 14
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    Landesman-Lazer resonance problems and saddle point methods (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 229-238 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show how saddle point techniques can be used to obtain new results for general resonance problems of the type considered by Landesman and Lazer.
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    URL: http://dx.doi.org/10.1002/mma.1670170402
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  • 15
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    The stationary and non-stationary stokes system in exterior domains with non-zero divergence and non-zero boundary values (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 269-291 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In an exterior domain Ω⊂∝n, n ≥ 2, we consider the generalized Stokes resolvent problem in Lq-space where the divergence g = div u and inhomogeneous boundary values u = ψ with zero flux ∫∂Ωψ·N do = 0 may be prescribed. A crucial step in our approach is to find and to analyse the right space for the divergence g. We prove existence, uniqueness and a priori estimates of the solution and get new results for the divergence problem. Further, we consider the non-stationary Stokes system with non-homogeneous divergence and boundary values and prove estimates of the solution in L5(0, T;Lq(Ω)) for 1 〈 s, q 〈 ∞.
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    URL: http://dx.doi.org/10.1002/mma.1670170405
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  • 16
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    Finite element approximation of a microstructure evolution (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 377-393 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The evolution model of a microstructure described as appropriately generalized Young measures, which was developed in [11], is discretized here by means of a suitably adapted finite element method. The convergence of the approximate solutions is proved, and a one-dimensional example is treated to discuss some implementation experience and to show some illustrative results.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170505
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  • 17
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    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    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.1670170601
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  • 18
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    Weak solutions of the initial-boundary value problem for the Vlasov-Poisson system (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 451-476 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we show the existence of a weak solution of the boundary value problem for the time dependent Vlasov-Poisson system. First, we regularize the system in order to apply a fixed-point theorem. Then we pass to the limit using an energy estimate.
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    URL: http://dx.doi.org/10.1002/mma.1670170604
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  • 19
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    Optimal control for parabolic systems with competitive interactions (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 509-524 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a two-dimensional parabolic system with general competitive interactions as a two-player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functional.
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    URL: http://dx.doi.org/10.1002/mma.1670170703
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  • 20
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    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    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.1670170801
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  • 21
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    Local existence of solutions to the Landau-Maxwell system (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 613-641 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study here the Landau-Maxwell system in its classical form. We prove the local existence of weak solution with initial data of unrestricted size. The main tools consist of an approximation method and a regularity result for velocity averages of solutions of some general linear transport equations.
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    URL: http://dx.doi.org/10.1002/mma.1670170804
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  • 22
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    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670170901
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  • 23
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    A finite element method and stabilization method for a non-linear tricomi problem (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 681-695 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove using the Faedo-Galerkin method the existence of a generalized solution of an initial-boundary value problem for the non-linear evolution equation0 ≤ Q ≤ 2, in a cylinder QT = Ω × (0, T), where T u = yuxx + uyy is the Tricomi operator and l(u) a special differential operator of first order. We then show that the approximate generalized solution of problem (*) converges to the approximate generalized solution of the corresponding stationary boundary value problem as t → ∞.
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    URL: http://dx.doi.org/10.1002/mma.1670170903
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  • 24
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    On a semi-coercive problem in a porous journal bearing with cavitation problem as boundary condition and subject to an integral condition (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 765-785 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a non-linear problem in pressure saturation modelling of a free boundary problem, arising in self-lubricating bearings, with Neumann boundary conditions for the pressure and a non-local constraint on the saturation variable, which indeed is a Lagrange multiplier. We prove an existence theorem by introducing an artificial time dependence and using the pseudo-characteristics discretization method and semi-coercive variational inequalities.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670171003
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  • 25
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    On stationary flow of asymmetric fluids with diffusion (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 837-854 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove existence and uniqueness theorems for weak solutions of equations describing stationary isothermic motion of a mixture of two viscous incompressible fluids with asymmetric stress tensor, in a bounded subset of ∝3. The model of the flow we consider here assumes that some of coefficients characterizing isotropic properties of the fluid equal zero.
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    URL: http://dx.doi.org/10.1002/mma.1670171102
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  • 26
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    Control problems with state constraints for shape memory alloys (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 943-952 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, two different control problems with state constraints for shape memory alloys are considered: in the non-isothermal case, we study boundary control problems, and in the isothermal situation, a dynamical shape optimization problem is considered. In both cases, the transverse displacement is the constrained state variable. The first-order conditions of optimality are derived.
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    URL: http://dx.doi.org/10.1002/mma.1670171204
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    Quantitative error estimates for coefficient idealization in linear elliptic problems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 971-987 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give a thorough quantitative error analysis for the effect of coefficient idealization on solutions of linear elliptic boundary value problems. The a posteriori error estimate is derived by a tactful application of the duality theory in convex analysis. The estimate involves an auxiliary function subject to certain constraint. We discuss in detail the selection of a good auxiliary function for various cases. Numerical examples show the effectiveness of our a posteriori error estimate.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670171206
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  • 28
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    An approximate Gidas-Ni-Nirenberg theorem (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1045-1052 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study positive solutions u to Δu + f(u) = 0 in Ω, u = 0 on ∂Ω, and we address the following question: If Ω is a small perturbation of a ball, is u a small perturbation of a radially symmetric function? We prove two theorems which give an affirmative answer under different assumptions on the non-linearity f and on the topologies in which perturbations are considered.
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    URL: http://dx.doi.org/10.1002/mma.1670171304
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    Diffusion limit for the linear boltzmann equation of the neutron transport theory (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1071-1087 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we present the asymptotic analysis of the linear Boltzmann equation for neutrons with a small positive parameter ∊ related to the mean free path, based upon the Chapman-Enskog procedure of the kinetic theory. We prove that if proper initial conditions derived by considering initial layer solutions are used, the diffusion equation gives the uniform approximation to the neutron density function with the O(∊2) accuracy.
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    URL: http://dx.doi.org/10.1002/mma.1670171306
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    Stability analysis of the phytoplankton vertical steady states in a laboratory test tube (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 551-575 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The positive vertical equilibrium profiles of a phytoplankton population growing in a vertical test tube under controlled experimental conditions (temperature, salinity, light intensity at the top surface) for nutrients are discussed with reference to their stability properties for arbitrary positive initial values of the biomass concentration along the tube. Two different approaches are followed. First a stability result is established in the Sobolev norm H2 by estimating the norms of the perturbations recursively in successive subintervals of suitably small amplitude. The second approach provides stability in the sense of the uniform convergence as a corollary of a stability theorem for a rather general class of integro-differential equations.
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    URL: http://dx.doi.org/10.1002/mma.1670170705
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    Non-linear stability for the Vlasov-Poisson system - the energy-Casimir method (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1129-1140 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of stability of stationary solutions of the Vlasov-Poisson system has received a lot of attention in the physics literature, both in the stellar dynamics and the plasma physics cases. The energy-Casimir method has been used to prove non-linear stability for various conservative systems, but no rigorous application to the Vlasov-Poisson system has been given yet. We employ this method to prove non-linear stability of stationary solutions for the plasma physics case in three geometrically different settings.
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    A non-isentropic Euler-Poisson model for a collisionless plasma (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 409-442 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We analyse transonic solutions of the one-dimensional Euler-Poisson model for a collisionless gas of charged particles in the non-isentropic steady-state case. The model consists of the conservation of mass, momentum and energy equations. The electric field is modelled self-consistently (Coulomb field). Boundary conditions on the particle density and particle temperature are imposed.The analysis is based on representing solutions piecewise as orbits in the particle-density-electric-field phase plane and connecting the orbit segments by the jump and entropy conditions.We characterize the set of all solutions of the Euler-Poisson problem. In particular, we show that, depending upon the length of the interval on which the boundary value problem is posed, fully subsonic, one-shock and (in certain cases) two-shock transonic and smooth transonic solutions exist. Also, numerical computations illustrating the structure of the solutions are reported.
    Additional Material: 21 Ill.
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    Resonance phenomena in a semi-infinite string with a periodic end (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 501-531 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in a semi-infinite string under the assumption that the material properties depend p-period-ically on the space variable outside a sufficiently large interval [0, a]. The spectrum of the self-adjoint extension A of the spatial part of the differential operator consists of a finite or countable number of bands and a (possibly empty) discrete set of eigenvalues located in the gaps of the continuous spectrum. We show that resonances of order t or t½, respectively, occur if either ω2 is an eigenvalue of A or (i) ω2 is a boundary point of the continuous spectrum of A and (ii) the corresponding time-independent homogeneous problem has a non-trivial solution which is p-periodic or p-semiperiodic for x 〉 a (‘standing wave’).
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    Relative entropy maximization and directed diffusion equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 545-554 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Motivated by the concept of maximum entropy methods in signal and image processing, we introduce and discuss a class of ‘directed diffusion equations’ with suitable boundary conditions. The paradigmatic ‘directed diffusion equation’ is The relative entropy \documentclass{article}\pagestyle{empty}\begin{document}$ Sb[f](t): = - \int_\Omega {f(t,x)} \;\ln \;(f(t,x)/b(x))dx $\end{document} is rapidly increasing along solution trajectories of (i). This suggests that solving (i) will yield efficient procedures for entropy maximization. We also discuss the asymptotic behavior of solutions of (i) - this is readily done because (i) has a large family of Ljapunov functionals.
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    A normal crack in an elastic half-space with stress-free surface (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 563-579 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: The problem of an elastic half-space with stress-free surface and a crack of arbitrary shape with prescribed displacements or tractions is reduced to an equivalent system of integral equations on the crack. For a pressurized crack in a plane perpendicular to the free surface, a scalar integral equation is derived. In properly chosen function spaces, unique solvability of the integral equation and regularity of solutions for regular data are proven.
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    Global existence for one-dimensional motion of non-isentropic viscous fluids (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 609-624 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We study the p-system with viscosity given by vt - ux = 0, ut + p(v)x = (k(v)ux)x + f(∫0x vdx, t), with the initial and the boundary conditions (v(x, 0), u(x,0)) = (v0, u0(x)), u(0,t) = u(X,t) = 0. To describe the motion of the fluid more realistically, many equations of state, namely the function p(v) have been proposed. In this paper, we adopt Planck's equation, which is defined only for v 〉 b(〉 0) and not a monotonic function of v, and prove the global existence of the smooth solution. The essential point of the proof is to obtain the bound of v of the form b 〈 h(T) ≤ v(x, t) ≤ H(T) 〈 ∞ for some constants h(T) and H(T).
    Additional Material: 1 Ill.
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    Classical solutions of two-dimensional stokes problems on non-smooth domains. Part 1: The radon integral operators (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 643-664 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The applicability of the Neumann indirect method of potentials to the Dirichlet and Neumann problems for the two-dimensional Stokes operator on a non-smooth boundary Γ is subject to two kinds of sufficient and/or necessary conditions on Γ. The first one, occurring in electrostatic, is equivalent to the boundedness on C(Γ) of the velocity double-layer potential W as well as to the existence of jump relations of potentials. The second condition, which forces Γ to be a simple rectifiable curve and which, compared to the Laplacian, is a stronger restriction on the corners of Γ, states that the Fredholm radius of W is greater than 2. Under these conditions, the Radon boundary integral equations defined by the above-mentioned jump relations are solvable by the Fredholm theory; the double- (for Dirichlet) and the single- (for Neumann) layer potentials corresponding to their solutions are classical solutions of the Stokes problems.
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    Boundary conditions in acoustic scattering with respect to the reciprocity relation (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 725-738 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: A new concept associated with the reciprocity relation in acoustic scattering is introduced. Motivated by this well-known relation, which holds in all the classical cases, more general boundary value problems for the scalar Helmholtz equation are studied. These generalized boundary conditions are characterized by the validity of the reciprocity relation and seem to be an appropriate unification of a large class of boundary value problems in acoustic scattering. The well-known results for the classical problems can be extended to this general case and also new connections with the question about existence and uniqueness of solutions to the boundary value problems can be derived. A constructive procedure shows that this approach is applicable for a large class of boundary conditions.
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    An Lq-theory for weak solutions of the stokes system in exterior domains (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 707-723 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We introduce a new concept for weak solutions in Lq-spaces, 1 〈 q 〈 ∞, of the Stokes system in an exterior domain Ω ⊂ ∝n, n ≥ 2. Defining the variational formulation in the homogeneous Sobolev space \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop H\limits^.{_{0}}^{1,q} (\Omega )^n = \{ u \in L_{1{\rm oc}}^q (\overline \Omega )^n;\nabla u \in L^q (\Omega )^{n^2 },u\left| {_{\partial \Omega } = 0} \right.\},$\end{document} we prove existence and uniqueness of weak solutions for an arbitrary external force and a prescribed divergence g = div u. On the other hand, solutions in the sense of distributions which are defined by taking test functions only in C0∞(Ω)n are not unique if q 〉 n/(n-1). In this case, a hidden boundary condition related to the force exerted on the body may be imposed to single out a unique solution.
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    Non-linear singular diffusion with non-linear boundary conditions (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 779-798 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Outgassing and contamination: Strict solution of a Boltzman-like model (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 799-817 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We consider a Boltzmann-like model of a problem of outgassing and contamination in a region R. For simplicity, we assume that R = R1 ∪ R2 ∪ R3, where R1 is the slab {x: -a 〈 x 〈 0}, R2 = {x:0 〈 x 〈 b}, R3 = {x: b 〈 x 〈 b1}. R1 is the region where the contaminant particles are produced, R2 is the ‘cavity’ where such particles migrate and interact with some inert gas, usually at low pressure, and R3 is the region which is contaminated by the particles coming from R2. In each of the three regions, the behaviour of the contaminant particles is represented by means of a Boltzmann-like equation.We prove that such a mathematical problem has a unique positive strict solution, belonging to a suitable Banach space Y. A system of ordinary differential equations is also derived, which gives the global balances of the contaminant particles in each of the three regions.
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    Solitary wave solutions and cnoidal wave solutions to the combined KdV and mKdV equation (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 339-347 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: This paper presents a mapping approach for the construction of exact solutions to the combined KdV and mKdV equation. There exist two types of soliton solutions which will reduce back to those of the KdV and mKdV equations in some appropriate limits. Four types of the general cnoidal wave solutions are also obtained.
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    General interface problems - II (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 431-450 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We continue the study of general interface problems. We prove regularity and asymptotics of solutions in usual Sobolev spaces for non-constant coefficients operators. We also give the stabilization procedure when unstable decompositions appear near a critical angle.
    Additional Material: 18 Ill.
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    On global solvability of non-linear viscoelastic equations in the analytic category (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 477-486 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: We prove the global existence of analytic solutions to the non-linear viscoelastic equations of the following type: \documentclass{article}\pagestyle{empty}\begin{document}$$ u_n \, = \,\phi \,(\,||\,\nabla _x \,u\,||^2)\Delta u\, + \,\Psi \,(||\,D_x^\beta \,1\,u\,||^2,\,.\,.\,.\,\,||\,D_{x^N }^\beta \,||)\,\Delta u_t $$\end{document} where φ and ψ are continuous and non-negative functions satisfying some additional conditions. The method of the analytic energy estimates is used.
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    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670171201
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    Stability and instability in adiabatic shearing motions of incompressible fluids (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 933-942 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We investigate the effect of temperature dependence of the viscosity on the stability of the adiabatic shearing flows of an incompressible Newtonian viscous fluid between two parallel plates. When the viscosity strongly decreases with temperature, the shearing flow caused by a steady motion of the upper plate (steady shearing) becomes unstable, while the shearing flow caused by a time-dependent body force is found to be stable.
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    Masthead (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Subsolutions and super solutions to systems of parabolic equations with applications to generalized Fujita-type systems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1005-1016 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: A constructive method for obtaining subsolutions and supersolutions to the Cauchy problem for systems of parabolic equations is discussed. Applications of the method to Fujita-type systems are considered leading to global existence and finite time blow-up results.
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    The existence of global in space variables solution for non-linear subelliptic equation of floating water (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1053-1070 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The existence of global in space variables solutions for a class of non-linear subelliptic evolution operators is proved. A Cauchy problem and an initial-boundary value problem are considered using the contraction theorem and Galerkin methods.
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    On the boundary transmission problem of thermoelastostatics in a plane domain with interface corners (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1089-1114 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: This paper deals with bimetal problems of thermoelastostatics. By means of an explicit particular solution a reduction to problems of elastostatics is given. An indirect boundary integral method is applied for solving the traction boundary value problem. The solution is represented by a potential of single layer type having Green's contact tensor as the kernel. Thus, from the first the transmission conditions are satisfied. The Fredholm property of the boundary integral operator as well as the asymptotics of the potential density at an interface corner depend on the symbol of a Mellin convolution operator. The singular functions at corners can be obtained by calculating the potential for terms in the asymptotic expansion of the density.
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    Stokes flow of a micropolar fluid exterior to several non-intersecting closed surfaces, but contained by an exterior contour (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1115-1127 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The problem of determining the Stokes flow of a micropolar fluid exterior to several closed surfaces but contained by an exterior contour that encloses all the interior surfaces, is formulated as a system of linear Fredholm integral equations of the second kind. These integral equations are obtained when the velocity and microrotation vector fields are represented by a double-layer potential with unknown density, and certain singular solutions of the Stokes' micropolar equations. This double-layer potential is defined over the union of all the surfaces involved including the exterior contour. The singularities, corresponding to a concentrated force and concentrated couple located within each interior surface, give rise to force and torque whose magnitudes are linearly dependent on the unknown density of the double layer. It is shown that the system possesses a unique continuous solution when the boundaries are Lyapunov surfaces and the boundary data is continuous.
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    Scattering results for measure potentials with unbounded support (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1213-1230 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The eigenfunction expansion theorem and its application to the scattering operator and the scattering matrix is extended to Schrödinger operators with measure potentials with unbounded support on ∝n that are known to generate wave operators that are strongly complete. Analyticity conditions of the eigenfunctions and the scattering matrix are presented.
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    A remark on a compactness result in electromagnetic theory (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 123-129 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Calderon's extension theorem is a crucial tool in the proof of the compactneσs of the resolvent for the Maxwell operator, and whence this result is proved for domains with the strict cone property. However, the proof only requires an extension operator that extends W2,2-functions compactly as W1,2-functions. It is shown that this can be achieved under weaker regularity conditions on the domain: the cone may be replaced by some cusp of an appropriate order.
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    Resonance frequencies of a cavity containing a compressible viscous fluid (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 185-202 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: The aim of this paper is to study the resonance spectrum of a cavity containing a compressible viscous fluid. This system admits a discrete infinite sequence of eigenvalues whose real parts are negative, which is interpreted as the damping effect introduced by viscosity. Only a finite number of them have non-zero imaginary parts and this number depends on viscosity; a simple criterion is given for their position in the complex plane. The case of a cavity containing an elastic mechanical system immersed in the fluid is also examined; from a qualitative point of view, the nature of the resonance spectrum remains unchanged.
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    The transient behaviour of multidimensional PN-diodes in low injection (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 265-279 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: An initial boundary value problem modelling the transient behaviour of a pn-junction semiconductor diode is simplified by formal asymptotics, where the scaled minimal Debye length and the scaled intrinsic number are considered as small parameters. The implicit assumption on the biasing situation is that of low injection. The simplified model is shown to be equivalent to an integral relation between the evolution of the current and of the contact voltage. A simple switching application is governed by a non-linear Volterra integral equation for the current. This equation is shown to possess a unique solution globally in time converging to the unique steady state.
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    Modelling of dynamic networks of thin elastic plates (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 379-407 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The purpose of this paper is to derive junction conditions for networks of thin elastic plates and to analyse the dynamic equations of such networks. Junction conditions for networks of Kirchhoff plates and networks of Reissner-Mindlin plates are derived based on geometric considerations of the deformation at a junction. It is proved that the dynamic system which describes the Reissner-Mindlin network is well-posed is an appropriate energy space. It is further established that the Kirchhoff network is obtained in the limit of the Reissner-Mindlin network as the shear moduli go to infinity.
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    The boundary equation method in the third initial boundary value problem of the theory of elasticity. Part 2: Methods for approximate solutions (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 217-227 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work considers the methods for solving approximately the four types of boundary equations arising when the third initial boundary value problem of the theory of elasticity is solved with the help of retarded elastic potentials. The convergence of these methods is proved.
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    URL: http://dx.doi.org/10.1002/mma.1670160305
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    An implicit finite-difference algorithm for the numerical simulation of supersonic flow over blunted bodies (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 229-263 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In order to compute axisymmetric laminar supersonic flow we use an unsteady implicit finite-difference scheme. This scheme solves numerically either the inviscid Euler equations or the ‘thin-layer’ Navier-Stokes equations. In both cases the scheme leads to large sparse non-linear systems, which can be solved by a genuine iteration process. The convergence of this process is shown and numerical results are given.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160402
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
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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.1670160501
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    General interface problems - I (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 395-429 
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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 transmission problems for elliptic operators of order 2m with general boundary and interface conditions, introducing new covering conditions. This allows to prove solvability, regularity and asymptotics of solutions in weighted Sobolev spaces. We give some numerical examples for the location of the singular exponents.
    Additional Material: 18 Ill.
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    Generalized spherical harmonics and exterior differentiation in weighted sobolev spaces (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1017-1043 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We generalize spherical harmonics expansions of scalar functions to expansions of alternating differential forms (‘q-forms’). To this end we develop a calculus for the use of spherical co-ordinates for q-forms and determine the eigen-q-forms of the Beltrami-operator on SN-1 which replace the classical spherical harmonics. We characterize and classify homogeneous q-forms u which satisfy Δu = 0 on ∝N﹨{0} and determine Fredholm properties, kernel and range of the exterior derivative d acting in weighted Lp-spaces of q-forms (generalizing results of McOwen for the scalar Laplacian). These techniques and results are necessary prerequisites for the discussion of the low-frequency behaviour in exterior boundary value problems for systems occurring in electromagnetism and isotropic elasticity.
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    URL: http://dx.doi.org/10.1002/mma.1670171303
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    Completeness of the wave operators in scattering of classical waves by local perturbations of a cone shaped domain (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1141-1164 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider wave propagation in a cone shaped unbounded domain which contains an inhomogeneous medium with non-smooth coefficients. Existence and completeness of the wave operators are proved in the case of local perturbations of the domain and the coefficients.
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    URL: http://dx.doi.org/10.1002/mma.1670171405
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    On a mathematical model for hot carrier injection in semiconductors (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1193-1212 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a collisionless transport model for electrons in a semiconductor, and we perform an asymptotic analysis for low temperatures or large applied biases. We derive analytic relations for the built-in potential and for the current which flows through the structure.
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    URL: http://dx.doi.org/10.1002/mma.1670171503
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
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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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    Modelling and solving fixed-bed adsorption (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 533-544 
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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 develop a mathematical model for packed-bed adsorption of a single component, directed toward the purification of β-lactamic antibiotics. The model describes the removal of sorbates from an aqueous stream entering a bed packed with spherical sorbent particles. Then, assuming that the adsorption isotherm is linear, an exact solution for this model is found.
    Additional Material: 1 Ill.
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    Global existence of classical solutions to the dynamical von Kármán equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 581-586 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: This paper derives an improved energy inequality for the non-linear dynamical von Kármán equations. The existence of global classical solutions is a consequence of this a priori inequality.
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    URL: http://dx.doi.org/10.1002/mma.1670160806
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    Weak solutions of the Vlasov-Poisson initial boundary value problem (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 587-607 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: This paper deals with existence results for a Vlasov-Poisson system, equipped with an absorbing-type law for the Vlasov equation and a Dirichlet-type boundary condition for the Poisson part. Using the ideas of Lions and Perthame [21], we prove the existence of a weak solution having good Lp estimates for moment and electric field, by a good control on the higher moments of the initial data. As an application, we establish a homogenization result in the Hilbertian framework for this type of problem in non-homogeneous media, following the work by Alexandre and Hamdache [2] for general kinetic equations, and Cioranescu and Mural [11] for the Laplace problem.
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    Classical solutions of two-dimensional stokes problems on non-smooth domains. Part 2: Collocation method for the radon equation (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 665-679 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The non-uniquely solvable Radon boundary integral equation for the two-dimensional Stokes-Dirichlet problem on a non-smooth domain is transformed into a well posed one by a suitable compact perturbation of the velocity double-layer potential operator. The solution to the modified equation is decomposed into a regular part and a finite linear combination of intrinsic singular functions whose coefficients are computed from explicit formulae. Using these formulae, the classical collocation method, defined by continuous piecewise linear vector-valued basis functions, which converges slowly because of the lack of regularity of the solution, is improved into a collocation dual singular function method with optimal rates of convergence for the solution and for the coefficients of singularities.
    Additional Material: 1 Ill.
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    On directed diffusion with measurable background (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 681-690 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We show that the ‘directed diffusion equation’ \documentclass{article}\pagestyle{empty}\begin{document}$$ b(x)\frac{{\partial u}}{{\partial t}}(t,\,\;x) = div(b^2 (x)\nabla _x u(t,\;x)), $$\end{document} with periodic boundary conditions has a unique weak solution u whenever b is measurable and bounded above and below by positive constants. Also, limt→∞u(t,x) in Lp, 1≤p≤∞.
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    The trend to a stationary state for the Lebowitz Stick model (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 739-757 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The asymptotic behaviour of the Lebowitz stick model in kinetic theory is studied in weak* measure, L1- and L∞-sense.
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
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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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    Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shellThis research was supported by the Alexander von Humboldt Foundation of the Federal Republic of Germany at the Mathematical Institute of the University of Cologne. (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 13-33 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The purpose of this paper is to study bifurcation points of the equation T(v) = L(λ,v) + M(λ,v), (λ,v) ∊ Λ × D in Banach spaces, where for any fixed λ ∊ Λ, T, L(λ,·) are linear mappings and M(λ,·) is a nonlinear mapping of higher order, M(λ,0) = 0 for all λ ∊ Λ. We assume that λ is a characteristic value of the pair (T, L) such that the mapping T - L(λ,·) is Fredholm with nullity p and index s, p 〉 s ≥ 0. We shall find some sufficient conditions to show that (λ,0) is a bifurcation point of the above equation. The results obtained will be used to consider bifurcation points of the axisymmetric buckling of a thin spherical shell subjected to a uniform compressive force consisting of a pair of coupled non-linear ordinary differential equations of second order.
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    Radially symmetric global classical solutions of non-linear wave equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 131-149 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Cauchy problem for semilinear wave equations utt - Δu + h(|x|)up = 0 with radially symmetric smooth ‘large’ data has a unique global classical solution in arbitrary space dimensions if h is non-negative and p any odd integer provided the smooth factor h vanishes with sufficiently high order at the origin and is bounded together with its derivatives.
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    Vector spherical spline interpolation - basic theory and computational aspects (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 151-183 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Vector spherical interpolation is discussed from both the theoretical and computational points of view. The theory of vector spherical harmonics is an essential tool. An estimate is given for the absolute error of the interpolation process; an efficient algorithm is developed for the computation of a vector spherical interpoiant. The displacement boundary value problem of determining the elastic field from a finite number of discretely given displacement vectors is solved by the use of vector splines.
    Additional Material: 3 Ill.
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    Stabilization estimates for penetrative motions in porous media (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 11-20 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The physical model for penetrative convection in porous media is here considered to study the effects of variation of the source parameters on the flow. In this note we study the continuous dependence upon the heat supply and the body force of the classical solutions to the initial-boundary value problem of a heat conducting fluid through a porous solid, both for the (well-posed) forward problem and for the (improperly posed) backward in time one. For the former problem we obtain a result of continuous dependence with respect to the L2 norm; while for the latter we prove a result of Hölder continuity in a suitably constrained class of solutions.
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    Polygonal interface problems for the biharmonic operator (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 21-39 
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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 some boundary value problems on two-dimensional polygonal topological networks, where on each face, the considered operator is the biharmonic operator. The transmission conditions we impose along the edges are inspired by the models introduced by H. Le Dret [13] and Destuynder and Nevers [9]. The boundary conditions on the external edges are the classical ones. This class of problem contains the boundary value problems for the biharmonic equation in a plane polygon (see [3, 11, 12, 18]). Conforming to the classical results cited above, we prove that the weak solution of our problem admits a decomposition into a regular part and a singular part, the latter being a linear combination of singular functions depending on the domain and the considered boundary value problem. Finally, we give the exact formula for the coefficients of these singularities.
    Additional Material: 3 Ill.
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    Resonance phenomena in infinite strings with periodic ends (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 115-154 
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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 propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in an infinite string under the assumption that the material properties are p1-periodic for x 〉 a and p2-periodic for x 〈 - a. As has been pointed out in two preceding papers devoted to related configurations ([4], [5]), the combination of a time-periodic force and a periodic spatial structure may lead to resonance phenomena. We show that the present configuration also permits resonances of orders t and t1/2 for a discrete set of frequencies. The occurrence of resonances is closely related to the presence of non-trivial solutions of the corresponding time-independent homogeneous problem which satisfy certain asymptotic properties (‘standing waves’).
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    Stability and asymptotic behaviour in a reaction-diffusion system (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 155-169 
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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 some qualitative analysis for a coupled system of five reaction-diffusion equations which arises from a physiology model. The uniform boundedness of the time-dependent solution is obtained under various boundary conditions. Sufficient conditions are also given to ensure the asymptotic stability of the non-negative steady-state solutions under Dirichlet or Robin boundary condition for each component. Under homogeneous Neumann boundary condition for some components the time-dependent solution is proven to converge to a constant steady state determined by the initial functions.
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    Bifurcations of strongly non-linear self-excited oscillations (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 189-207 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Perturbation of a single-degree-of-freedom conservative oscillator leads to the emergence and vanishing of periodic solutions and to various types of self-excited oscillations. Using techniques from dynamical systems theory, in particular a certain Poincaré map, we establish the presence of Hopf bifurcations, various types of homoclinic bifurcations and saddle-node bifurcations of the associated Poincaré map. The corresponding bifurcation sets in parameter space are computed explicitly by perturbation methods. The theory is applied to the generalized van der Pol and the generalized Rayleigh oscillator, and to the case of a non-linear spring attached to a conveyor belt.
    Additional Material: 7 Ill.
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    An approximation theorem in inverse electromagnetic scattering (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 293-303 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the inverse electromagnetic scattering problem for an inhomogeneity of compact support with constant permittivity Colton and Päivärinta suggested an optimization scheme which yields a numerical method for determining the refractive index if the far-field data of the scattering problem is known [1]. We prove the denseness of the Cauchy data to certain interior transmission problems and conclude that the infimum of the optimization scheme is zero even if the permittivity varies. Before proving the denseness result, we investigate a boundary value problem which is needed to prove the denseness result.
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    A principle of linearization and the uniform asymptotic stability of solutions of the Navier-Stokes equations for compressible isothermic fluidsThis research was supported by the Alexander von Humboldt Foundation during the stay of the author at the University of Würzburg and the Technical University Darmstadt, FRG. (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 251-267 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the correctness of a principle of linearization in the investigation of the uniform asymptotic stability of a sufficiently smooth, but generally non-steady, solution of the Navier-Stokes equations for compressible fluids in the case of a constant temperature.
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    Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and Schrödinger-Poisson systems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 349-376 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove global existence and uniqueness of classical solutions of the Wigner-Poisson and Schrödinger-Poisson systems of equations for both repulsive and attractive potentials. In the repulsive case, we prove decay estimates for the particle density, the potential and the solutions.
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    A posteriori error analysis for linearization of nonlinear elliptic problems and their discretizations (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 487-508 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper is devoted to a posteriori quantitative analysis for errors caused by linearization of non-linear elliptic boundary value problems and their finite element realizations. We employ duality theory in convex analysis to derive computable bounds on the difference between the solution of a non-linear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on differences between finite element solutions of the nonlinear problem and finite element solutions of the linearized problem, by using finite element solutions of the linearized problem only. Numerical experiments show that our a posteriori error bounds are efficient.
    Additional Material: 2 Ill.
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    A hyperbolic - parabolic system modelling the thermoelastic impact of two rods (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 901-918 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The dynamic thermoelastic impact of two rods is modelled by a coupled system of two quasivariational inequalities and two equalities that reflect a bilateral contact condition and a radiation condition for the temperatures. The existence of a weak solution is established using a penalization method that employs Galerkin approximations and a priori estimates.
    Additional Material: 1 Ill.
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
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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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    Modelling of dynamic networks of thin thermoelastic beams (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 327-358 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We derive a distributed-parameter model of a thin non-linear thermoelastic beam in three dimensions. The beam can also be initially curved and twisted. Our main task is to formulate the non-homogeneous initial, boundary and node value problem associated with the dynamics of a network of a finite number of such beams. The emphasis here is on a distributed-parameter modelling of the geometric and kinematic node conditions. The forces and couples appearing in the boundary and node conditions can then be viewed as control variables. The analysis of the resulting control systems and their controllability and stabilizability properties is the subject of [25] and of forthcoming papers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160503
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    Decay properties of periodic, radially symmetric solutions of Sine-Gordon-type equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 359-378 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the radially symmetric, nonlinear wave equation and discuss the asymptotic behaviour as r → ∞ of solutions which are T-periodic in time t. It is shown that only two possibilities of decay can arise, namely polynomial like t-½(n-1) and exponential e-bt for some b 〉 0. Existence results are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160504
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    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.1670160701
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    Study of global solutions of parabolic equations via a priori estimates. Part I: Equations with principal elliptic part equal to the laplacian (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 457-474 
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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 global solutions of ut=Δu + f(u, Du) with zero boundary data. Under suitable hypotheses on f, we show that an energy, which is roughly the H1 norm of u, cannot change too rapidly. When f depends only on u, this estimate implies that all global solutions are bounded.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160702
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    Parameter-dependent operator equations of the Riccati type with application to transport theory (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 475-500 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We obtain an existence result for global solutions to initial-value problems for Riccati equations of the form R′(t) + TR(t) + R(t)T = Tρ A(t)T1-ρ + Tρ B(t)T1-ρ R(t) + R(t)TρC(t) T1-ρ + R(t)TρD(t)T1-ρ R(t), R(0)=R0, where 0 ≤ ρ ≤ 1 and where the functions R and A through D take on values in the cone of non-negative bounded linear operators on L1 (0, W; μ). T is an unbounded multiplication operator. This problem is of particular interest in case ρ = 1 since it arisess in the theories of particle transport and radiative transfer in a slab. However, in this case there are some serious difficulties associated with this equation, which lead us to define a solution for the case ρ = 1 as the limit of solutions for the cases 0 〈 ρ 〈 1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160703
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    The existence and regularity of solutions to the non-linear equation of flotating water (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 555-562 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of solutions to the nonlinear equations including the equation of flotating water is proved using the subellipticity of an operator in the equation and the contraction argument. Moreover a regularity result is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160804
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    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.1670160901
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    Evolution of a microstructure: A convexified model (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 625-642 
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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 known that, in a steady-state case, the variational principle of minimal non-convex potential energy creates a microstructure. This paper tries to formulate evolution of such microstructure on a basis of an energy variational principle (of the Hamilton type) involving a kinetic and a Rayleigh dissipative energies with the generalized impulse respecting a ‘convexified’ geometry. The existence of a solution is proved, using an approximation by a semi-discretization in time. Some quantitative properties are investigated, too.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160903
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    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.1670161001
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    Exact and approximate boundary conditions at artificial boundaries (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 691-705 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The use of transformation methods for the derivation of boundary conditions at artificial boundaries had been initiated by Engquist and Majda [4. 5]. They considered the scalar wave equation and strictly hyperbolic systems. This has been extended by Gustafsson [11] to inhomogeneous conditions, by Hagstrom [15] to parabolic and Halpern et al. [17, 20] to incompletely parabolic systems. Here a systematic method is developed which unifies these approaches. Additionally, inhomogeneities with non-compact support are taken into account. Exact and first-order approximate boundary conditions for the compressible Navier-Stokes equations are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161003
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    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.1670161101
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    A mathematical model for diffusion and exchange phenomena in ultra napkins (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 759-777 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The performance of napkins is nowadays improved substantially by embedding granules of a superabsorbent into the cellulose matrix. In this paper a continuous model for the liquid transport in such an “ultra napkin” is proposed. Its mean feature is a non-linear diffusion equation strongly coupled with an ODE describing a reversible absorption process. An efficient numerical method based on a symmetrical time splitting and a finite difference scheme of ADI-predictor-corrector type has been developed to solve these equations in a three-dimensional setting. Numerical results are presented that can be used to optimize the granule distribution.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161102
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    Singularity functions at axisymmetric edges and their representation by Fourier series (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 837-854 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The regularity of solutions of the Dirichlet problem for the Poisson equation in three-dimensional axisymmetric domains with reentrant edges is studied by means of Fourier series. The decomposition of the 3D problem into variational equations in 2D, a priori estimates of their solutions, a theorem of Riesz-Fischer type and two singularity functions (of tensor and non-tensor product type) are given.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161202
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    Interface problem in holonomic elastoplasticity (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 819-835 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The three-dimensional interface problem with the homogeneous Lamé system in an unbounded exterior domain and holonomic material behaviour in a bounded interior Lipschitz domain is considered. Existence and uniqueness of solutions of the interface problem are obtained rewriting the exterior problem in terms of boundary integral operators following the symmetric coupling procedure.The numerical approximation of the solutions consists in coupling of the boundary element method (BEM) and the finite element method (FEM). A Céa-like error estimate is presented for the discrete solutions of the numerical procedure proving its convergence.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161105
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