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  • Articles  (100)
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  • Articles: DFG German National Licenses  (100)
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  • 1985-1989  (38)
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  • Mathematics  (100)
  • 1
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    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 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider 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 
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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 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 
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    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.
    Type of Medium: Electronic Resource
    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
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160603
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  • 8
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in a semi-infinite string under the assumption that the material properties depend p-period-ically on the space variable outside a sufficiently large interval [0, a]. The spectrum of the self-adjoint extension A of the spatial part of the differential operator consists of a finite or countable number of bands and a (possibly empty) discrete set of eigenvalues located in the gaps of the continuous spectrum. We show that resonances of order t or t½, respectively, occur if either ω2 is an eigenvalue of A or (i) ω2 is a boundary point of the continuous spectrum of A and (ii) the corresponding time-independent homogeneous problem has a non-trivial solution which is p-periodic or p-semiperiodic for x 〉 a (‘standing wave’).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160704
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  • 9
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160803
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  • 10
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160805
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  • 11
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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    URL: http://dx.doi.org/10.1002/mma.1670160902
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  • 12
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670160904
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  • 13
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161005
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  • 14
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161004
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  • 15
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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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    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.1670161103
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  • 16
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670161104
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  • 17
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670160205
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  • 18
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    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.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160303
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  • 19
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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.1670160401
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  • 20
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670160403
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  • 21
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The purpose of this paper is to 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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    URL: http://dx.doi.org/10.1002/mma.1670160602
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  • 22
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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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    ISSN: 0170-4214
    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.
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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
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    URL: http://dx.doi.org/10.1002/mma.1670160501
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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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    URL: http://dx.doi.org/10.1002/mma.1670160801
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  • 26
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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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    URL: http://dx.doi.org/10.1002/mma.1670160802
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  • 27
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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
    Source: Wiley InterScience Backfile Collection 1832-2000
    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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    URL: http://dx.doi.org/10.1002/mma.1670160807
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670161006
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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
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    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
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    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.
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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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    URL: http://dx.doi.org/10.1002/mma.1670160301
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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
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    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.
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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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    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.
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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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    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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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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.
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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 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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.
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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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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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.
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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
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    Topics: Mathematics
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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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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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.
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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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    Exact and approximate boundary conditions at artificial boundaries (1993)
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    Mathematical Methods in the Applied Sciences 16 (1993), S. 691-705 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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.
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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
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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 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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.
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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 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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.
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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 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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.
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    Initial-boundary value problems for non-linear equations of generalized thermoelasticity and elasticity (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 49-60 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We formulate a local existence theorem for the initial-boundary value problems of generalized thermoelasticity and classical elasticity. We present a unified approach to such boundary conditions as, for example, the boundary condition of traction, pressure or place combined with the boundary condition of heat flux or temperature.
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    Low Reynolds number deformation of compound drops in shear flow (1993)
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    Mathematical Methods in the Applied Sciences 16 (1993), S. 61-74 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The method developed by Rallison and Acrivos (1978) to solve the deformation of a single drop due to exterior shear flow for a small Reynolds number is extended to the problem of the deformation of a compound drop. The result is found in terms of a Fredholm integral equation of the second kind, which is shown to have a unique solution and the solution is given by means of a uniformly convergent Neumann series.
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    One gauge-invariant system for two-dimensional relativistic fields: Global solutions, integrability (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 115-122 
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    Notes: The system originating from the theory of two-dimensional hyperbolic chiral fields and the theory of self-dual Yang-Mills fields over ∝2 + 2 is studied. The existence of global solutions for the Cauchy problem is established. It is observed that the system is completely integrable and one method of construction of a new solution is presented.
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    Boundary integral solution of the two-dimensional heat equationThis research was started while the second author was visiting professor at the University of Delaware in the Spring of 1989. (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 87-114 
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    Notes: Here we consider initial boundary value problems for the heat equation by using the heat potential representation for the solution. Depending on the choice of the representation we are led to a solution of the various boundary integral equations. We discuss the solvability of these equations in anisotropic Sobolev spaces. It turns out that the double-layer heat potential D and its spatial adjoint D′ have smoothing properties similar to the single-layer heat operator. This yields compactness of the operators D and D′. In addition, for any constant c ≠ 0, cI + D′ and cI + D′ are isomorphisms. Based on the coercivity of the single-layer heat operator and the above compactness we establish the coerciveness of the hypersingular heat operator. Moreover, we show an equivalence between the weak solution and the various boundary integral solutions. As a further application we describe a coupling procedure for an exterior initial boundary value problem for the non-homogeneous heat equation.
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    The boundary equation method in the third initial boundary value problem of the theory of elasticity. Part 1. Existence theorems (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 203-215 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: This work deals with four variants of boundary equations appearing if the third main initial boundary value problem is solved with the help of elastic retarded potentials. The solvability of these equations is proved, and the smoothness of their solutions researched.
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    Non-linear parabolic problem associated with the penetration of a magnetic field into a substance (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 281-295 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We study the following initial and boundary value problem: In section 1, with u0 in L2(Ω), f continuous such that f(u) + ∊ non-decreasing for ∊ positive, we prove the existence of a unique solution on (0,T), for each T 〉 0. In section 2 it is proved that the unique soluition u belongs to L2(0, T; H01 ∩ H2) ∩ L∞(0, T; H01) if we assume u0 in H01 and f in C1(∝,∝). Numerical results are given for these two cases.
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    Taylor expansions for distributions (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 297-304 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present the Taylor asymptotic expansion of a perturbed distribution of the form is a smooth function defined in ∝n. First we present the one-dimensional theory to illustrate the underlying concepts and then we discuss the multi-dimensional case. We find that various known results follow as special limits of our results.
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    Long-time behaviours of the spatially uniform discrete nagumo model (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 305-325 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a spatially uniform discrete Nagumo model is considered. The relation between the number and positions of period-2 solutions, and the parameter and initial values are discovered. The long-time behaviours of the solutions are discussed for different parameters and initial values.
    Additional Material: 9 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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    URL: http://dx.doi.org/10.1002/mma.1670160601
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    Iterative solution of linear systems arising from the Nyström method for the double-layer potential equation over curves with corners (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 443-455 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider a quadrature method for the solution of the double-layer potential equation corresponding to Laplace's equation in a polygonal domain. We prove the stability for our method in case of special triangulations over the boundary of the polygon. For the solution of the corresponding system of linear equations, we consider a two-grid iteration and establish the rates of convergence and complexity. Finally, we discuss the effect of mesh refinement near the corners of the polygon.
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    On a non-stationary Ginzburg-Landau superconductivity model (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 855-875 
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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 study a non-stationary superconductivity model derived from Ginzburg-Landau macroscopic theory. By using gauge invariance and studying a linear problem with curl boundary conditions, we obtain the existence of solutions. The solution is unique in the sense of gauge equivalence.
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    URL: http://dx.doi.org/10.1002/mma.1670161203
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    A solution formula for a non-convex scalar hyperbolic conservation law with monotone initial data (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 895-902 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we prove an explicit representation formula for the solution of a one-dimensional hyperbolic conservation law with a non-convex flux function but monotone initial data. This representation formula is similar to those of Lax [10] and Kunik [7,8] and enables us to compute the solution pointwise explicitly. This result is a generalization of a theorem given in Kunik [8] where the case of only one inflexion point for the fluxes was considered. Its proof uses the polygonal method of Dafermos [2]. The application of this method leads to a simple explicit construction of the solutions for a Kynch sedimentation process [9] and to an explicit parameter representation for the shock curves evolving during the sedimentation process.
    Additional Material: 3 Ill.
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    On the low wave number asymtotics for the two-dimensional exterior dirichlet problem for the reduced wave equationDedicated to E. Martensen on the occasion of his 60th birthday (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 335-341 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new proof is given for the low wave number asymptotics for the solutions to the exterior Dirichlet problem for the reduced wave equation in two dimensions.
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    URL: http://dx.doi.org/10.1002/mma.1670090126
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    Diffraction d'une Onde Acoustique par une Paroi Absorbante: Nouvelles Equations Intégrales (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 431-454 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present here a new formulation of the exterior Robin problem of the reduced wave equation, using boundary integrals with the jumps of the function and its normal derivative as variables. Our system of integral equations present an important advantage for any numerical purpose: it can be transformed in a variational problem where the sesqui-linear form is coercive and is exempt of hyper singular integrals.
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    URL: http://dx.doi.org/10.1002/mma.1670090131
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    An integral equation of the first kind for a free boundary value problem of the stationary Stokes' equations (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 550-575 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate a free boundary value problem of the stationary Stokes' equations. In a previous paper adapted hydrodynamical potentials have been constructed and their jump relations have been discussed. Here we study a direct method to obtain an equivalent boundary integral equations' system of the first kind. Its solution properties are investigated in the framework of strongly elliptic pseudodifferential operators. For numerical purposes a suitable representation formula for the variational equation is given in terms of integro-differential operators which avoids the evaluation of hypersingular integrals.
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    URL: http://dx.doi.org/10.1002/mma.1670090135
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    Evolution systems in semiconductor device modeling: A cyclic uncoupled line analysis for the gummel map (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 455-492 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The initial/boundary-value problem for isothermal, lattice, semiconductor device modeling is described and analyzed. This nonlinear elliptic/parabolic system of reaction/diffusion/convection type is determined by a Maxwell equation, relating space/charge and the electric field, and by two continuity equations for the free electron and hole carrier concentrations. The Einstein relations for Brownian motion are not assumed in this analysis, so that the electrostatic potential, u, and the carrier concentrations, n and p, are the fundamental dependent variables of the system. The boundary conditions are Dirichlet conditions for dependent variable values on the contact portions of the device, and homogeneous Neumann conditions, expressing insulation, on the complement. Complicating the analysis are the transition singularity points between the mixed boundary conditions, and the field dependence of the mobility and diffusion coefficients. By means of a physically motivated analysis of the convective current component, we are able to uncouple the system by a cyclic horizontal line analysis, without an unreasonable time step restriction. The corresponding linear equations are solved by a contractive inner iteration. The outer iteration is shown to converge to a unique solution of the system, under singularity classification at the transition points. The definition of this outer iteration follows the steady-state Gummel iteration at discrete time steps. An existence theory is a by-product of the analysis, and is separated from uniqueness theory.
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    Plane potential flow past a cylinder with porous surface (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 587-605 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: In the paper two models for the potential flow past a cylinder with porous or perforated surface are reduced to nonlinear Riemann-Hilbert problems for the complex velocity function and general existence and uniqueness theorems for the solution of the problems are derived. Further the problems are reduced to nonlinear singular integral equations of Hilbert type whose solvability is investigated by means of the Schauder and Banach fixed point theorem.
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    On a class of probability distributions (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 210-219 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The application of a three parameter class of one-sided probability distributions is being discussed. For specific parameter values, this class contains as special cases a number of well-known distributions of statistics and statistical physics, namely, Gauss, Weibull, exponential, Rayleigh, Gamma, chi-square, Maxwell, and Wien (limiting case of Planck's distribution). One of the three parameters represents scale; the other two represent initial and terminal shape of the associated probability density function. A fourth parameter, shift, may be introduced. The distribution class discussed in this paper was introduced by L. Amoroso [2] in 1924. It is closely connected with a family of linear Fokker-Planck equations (generalized Feller equation). In fact, the class of probability density functions associated with the distribution class considered here is a special case of the set of all delta function initial condition solutions of the generalized Feller equation for a fixed value of the time variable. It will be shown that, as a function of the logarithm of the independent variable, the logarithm of the cumulative distribution function is asymptotically linear as the independent variable approaches zero from above. This fact leads to a general criterion for the applicability of the presented distribution family relative to given empirical data. The applicability criterion can be used to determine approximate values for the two shape parameters. They can subsequently be used as initial values in any of the established parameter estimation techniques.
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    Some algorithms of the projective-Newton method for the finite element space (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 1-12 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The paper presents the projective-Newton method in the finite element space with curved finite elements along the boundary. The properties of this method are studied when the integrals are calculated by numerical quadrature. Some algorithms are derived when ω = {x ∊ R2: 0 〈 x1, x2 〈 1}.
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    High velocity particles in a collisionless plasma (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 46-52 
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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: We prove that smooth solutions of the relativistic Vlasov-Maxwell equations exist for all time provided the kinetic energy density is uniformly bounded.
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    Motion of a vibrating string in the presence of a convex obstacle: A free boundary problem (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 276-297 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Here we study the motion of a vibrating string in the presence of an arbitrary obstacle. We show that if the string always rebounds on the concave parts of the obstacle, it can either rebound or roll on the convex parts. The latter is the case if the velocity of the string is null at the contact point just before contact, or if the contact point propagates at a characteristic speed. Four examples are given. The three first correspond to the same obstacle, a sinusoidal arc, but with different initial conditions. In the first case, the string rebounds on the whole of the obstacle and the motion is explicitly determined when it is periodic. In the second case, the string rolls on the convex part of the obstacle up to the inflexion point and then rebounds on the concave part and unwinds on the convex part. In the third case, the string is initially at rest on the obstacle; then it instantaneously leaves the concave part while it unwinds progressively on the convex part. The fourth case is similar to the third but with a different obstacle; the motion, which is periodic, is determined explicitly.
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    On approximation to convective diffusion equation (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 399-412 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A closed-form analytical solution for the problem of homogeneous and heterogeneous reactions in a isothermal non-Newtonian laminar flow tubular reactor is presented. A technique is evolved where Galerkin method is applied in Laplace-transformed domain.
    Additional Material: 4 Ill.
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    A free boundary problem for three-dimensional harmonic vector fields (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 367-398 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study in this paper a free boundary value problem (FB), where a region Go in R3 is determined by the condition that there exists a vector field vo in Go which satisfies div vo = eo, curl vo = go in Go and vo = E on the boundary ∂Go with a given scalar function eo and given vector fields go and E. We give two equivalent formulations for this problem. Then we characterize the solutions by a non-linear integral equation. In order to solve the latter by a Newton method we linearize this equation. We investigate the ensuing linear integral equation. In case of axisymmetric configurations this is a singular integral equation whose index can be easily determined from the given data. We obtain a related equation, if we try to construct a field v in a region G which is on the boundary perpendicular to a given field B. Finally we use this method to investigate an astrophysical problem, which arises in the theory of pulsar magnetospheres.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670090128
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    The Galerkin-averaging method for nonlinear, undamped continuous systems (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 520-549 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The analysis of initial-boundary value problems for nonlinear evolution equations with a small parameter is carried out by projection and averaging. The complications of the extension to a second order approximation is discussed and subsequently demonstrated for the perturbed Klein-Gordon equation. The difference between the case of resonance and nonresonance at first order is emphasized.
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    Über das homogene Dirichlet-Problem bei nichtlinearen partiellen Differentialgleichungen vom Typ der Boussinesq-Gleichung (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 493-519 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Semilinear equations of Boussinesq type, e.g. utt + uxx - uxxxx + (u2)xx = 0, utt + uxx - uxxxx + uxuxx = 0, or certain equations containing the squared wave operator, e.g. uxxtt - uk = 0, k ∊ N k ≥ 2, are studied. A generalized boundary value problem on bounded domains can be treated using Hilbert space methods. The linear parts of these equations are not elliptic, the latter not even hypoelliptic. A mountain pass lemma is used to prove the existence of nontrivial weak solutions. These solutions are obtained in anisotropic Sobolev spaces.
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    Weak travelling fronts for population models with density dependent dispersion (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 576-586 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Approximation dans un Problème de Viscoélasticité PériodiqueCe travail a été effectué durant le séjour de l'auteur, en tant qu'associé, au laboratoire d'Analyse numérique et Mécanique de l'Université de Rennes I. (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 606-626 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We are concerned with equations which derive from a quasistatic periodic problem of viscoelasticity. We give a condition which yields to existence and uniqueness of a periodic solution. Then we prove a finite element method based on equilibrium elements for the space approximation and on the explicit Euler scheme for the time approximation.
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    Stability of a layer of dipolar fluid heated from below (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 35-45 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The equations of Bleustein and Green [2] are formulated in a way suitable to describe the convective instability which occurs when a layer of dipolar fluid is heated from below. The linear instability boundary is shown to coincide with the nonlinear stability curve and the critical Rayleigh numbers describing this boundary are found; in particular, the non-dimensional micro-length is found to always stabilize.
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    On finite displacements of circular elastic membranes (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 76-98 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    A potential well theory for the heat equation with a nonlinear boundary condition (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 127-136 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The present paper employs potential well arguments of a previous work by the authors [6] to obtain a sharp existence-nonexistence alternative for solutions to the linear heat equation subject to a non-linear boundary condition.
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    Resonances and standing waves (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 105-126 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recent investigations on aperiodic waves, which are generated by time-harmonic forces in waveguides, indicate a close relationship between resonances and certain time-harmonic solutions of homogeneous boundary value problems for the wave equation (“standing waves”). This paper is motivated by the observation that, in all known cases, standing waves are connected with resonances if and only if they are subject to suitable asymptotic restrictions as |x| → ∞. These asymptotic properties are used to introduce a class of “admissible” standing waves. We prove that admissible standing waves do not exist in a certain class of local perturbations Ω of the n-dimensional domain Ω0 bounded by the hyperplanes xn = 0 and xn = π. This extends a result of M. Faulhaber on the absence of eigenvalues. As we shall show in a subsequent paper, absence of admissible standing waves implies absence of resonances.
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    Sur l'Analyse Numérique des Equations de Hamilton-Jacobi-Bellman (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 198-209 
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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 the convergence in the L∞ norm of the approximation by finite element of the Hamilton-Jacobi-Bellman equation.The proof uses the subsolution's method and the notion of discret regularity. Since the submission, the optimal result has been obtained.
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    A free boundary problem and stability for the circular plate (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 240-250 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the recent paper [6] we have answered the question of stability for the nonlinear beam which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. The basic idea that was first used in a numerical solution and subsequently in the mathematical analysis was to consider the free boundary problem in the interval in which the beam is not in contact with the obstacle. In this work we consider the analogous problem for the linear circular plate. Numerical computations are crucial here to establish conditions essential for the problem of stability and they also yield the critical parameter values, i.e., the secondary bifurcation points.
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    The Helmholtz equation in disturbed half-spaces (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 312-323 
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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 boundary value problems for the Helmholtz equation in domains with boundaries coinciding with a plane outside a sufficiently large sphere. As opposed to the method of Gartmeier [6] (see also [12]) our analysis leads to an integral equation of the second kind with a compact operator. In the last chapter we study the set of far field patterns which are generated by entire incident fields.
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    On the initial layer and the existence theorem for the nonlinear Boltzmann equation (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 342-366 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The truncated Hilbert expansion including the initial layer terms is considered. This enables us to replace the singulary perturbed Boltzmann equation by a weakly nonlinear equation. In this way the existence of a strong solution of the Boltzmann equation is obtained for initial data close enough to a local Maxwellian. The solution exists in the physically significant time interval on which smooth solutions to the Euler equations exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090127
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    Time optimal boundary controllability of a simple linear viscoelastic liquid (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 413-430 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A viscoelastic liquid confined between two parallel plates is considered under the action of L2 (O, T)-boundary controls. Applying Laplace-Transform-techniques it is shown that L2 (O, l)-states are exactly controllable in finite time, depending on the speed of propagation of singularities. Finally the existence of time-optimal controls respecting a given norm bound is shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090130
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    Zu einigen mathematischen problemen in der theorie der transonischen strömung (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 177-197 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The work deals with a definition of a weak solution of steady plane transonic flows past a thin profile, with the properties of the solution across a shock wave, and with a derivation of a conservative difference scheme suitable for numerical solution of the above mentioned problem by a finite difference method. The work presents several examples of numerical solution of transonic flows past a profile, through a plane cascade and some three-dimensional results. The numerical results presented are compared with experimental results or with numerical results by other authors.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090114
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    Study of an elliptic problem with nonlinear boundary conditionsDedicaced to Joachim A. Nitsche on the occasion of his 60th birthday (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 261-275 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the problem of finding on a trapezium a harmonic function u the normal derivative of which is equal on one side to λ exp(u). We prove the existence of a solution branch (λ,u(λ)) with a turning point and, for the case of the square, the presence of bifurcations. The “inverse power” algorithm converges on a part of the branch.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090121
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    Masthead (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987) 
    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.1670090101
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    Finite time blow-up and stability properties of materials with fading memory (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 13-34 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A detailed analysis of the equations of nonlinear elasticity is carried out for a certain class of initial-boundary value problems.In particular, I examine whether the presence in the differential equation of a mechanical mechanism of dissipation is able to prevent instabilities and ensure global existence in time of the solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090103
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    Ästhetische rechtecksmaße, die maßstabsunabhängig sind (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 53-58 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An aesthetical measure of rectangles which is continuous and does not depend on the scale must be classical. There exist non classical measures which are scale-independent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090106
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    On the geometric form of solutions of a free boundary problem involving galvanization (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 99-104 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In [6], T. I. Vogel studied a free boundary problem originating in the galvanization process. He showed that if the given boundary Γ* is starlike or convex, then so is the free boundary solution Γ. Our purpose is to generalize Vogel's second result by showing (under certain assumptions) that Γ cannot have more (local) maxima or minima (relative to a given direction) than Γ*; also that Γ cannot have more inflection points or greater total curvature than Γ*. The author has already proven analogous results for the Bernoulli free boundary problem in [1], [2] and [3].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090109
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    Stationary solutions of the vlasov-fokker-planck equation (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 169-176 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study stationary solutions of the Vlasov-Fokker-Planck Equation, a modification of the Vlasov-Poisson Equation, obtained by adding a diffusion term with respect to velocity. From a physical point of view it describes a plasma in thermal equilibrium.We prove existence of stationary solutions; for the mollified equation even an existence- and uniqueness theorem holds for sufficiently high temperature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090113
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    Optimization models for the force and energy in competitive sports (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 298-311 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A general optimal control model for running and swimming is developed, whose principal parameters are the energy reserves, the breathing rate and the force. This model is then applied to the world records in these disciplines. It describes the data very well and the parameters employed have values, which agree closely with those obtained by other means.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090123
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    The electrostatic potential of spherical polyelectrolytes in aqueous solution (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 324-334 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The electrostatic potential in systems of spherical polyelectrolytes is determined by superposition of spherically symmetric solutions of the linearized Poisson-Boltzmann equation. The case of constant surface potential is investigated in detail. Higher-order approximations are given by use of a generalization of the addition theorem for modified Bessel functions.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090125
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    On the convergence of the spline collocation with discontinuous data (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 59-75 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article we study the convergence of the collocation method in the case where the smoothest splines are used as trial functions. The given data is allowed to be piecewise continuous. Our model problem is stated by means of an explicit Fourier representation in the space of periodic functions. Thus the results are applicable e.g. to differential operators and to classical integral operators of the convolutional type. Error estimates are given for a class of Sobolev norms. An application to the single layer potential is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090107
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    On an iterative method for a class of integral equations of the first kind (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 137-168 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we investigate an iterative method which has been proposed [1] for the numerical solution of a special class of integral equations of the first kind, where one of the essential assumptions is the positivity of the kernel and the given right-hand side. Integral equations of this special type occur in experimental physics, astronomy, medical tomography and other fields where density functions cannot be measured directly, but are related to observable functions via integral equations. In order to take into account the non-negativity of density functions, the proposed iterative scheme was defined in such a way that only non-negative solutions can be approximated. The first part of the paper presents a motivation for the iterative method and discusses its convergence. In particular, it is shown that there is a connection between the iterative scheme and a certain concave functional associated with integral equations of this type. This functional can be interpreted as a generalization of the log-likelihood function of a model from emission tomography. The second part of the paper investigates the convergence properties of the discrete analogue of the iterative method associated with the discretized equation. Sufficient conditions for local convergence are given; and it is shown that, in general, convergence is very slow. Two numerical examples are presented.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/mma.1670090112
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    On the approximation method of solving integral equations in diffusion problems (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 220-230 
    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 the one-dimensional problem of heat or mass transport in the system with moving ends. We show that without solving the heat transfer equation, the heat flux flowing out from the system can be found when temperature on the boundary of this system is known. We make use of the Banach contraction theorem for appropriate integral equations. Our method also enables us to find the distribution of temperature in the whole domain that forms the physical system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090117
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    On an initial boundary-value problem for a model system of equations of a granulated medium (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 231-239 
    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 an initial boundary-value problem for the system of equations describing the motion of a granulated medium with constant density.We introduce the notion of a weak solution of the problem and prove the existence of such a solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090118
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    Blow-up of solutions of the gain-term-only Boltzmann equation (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 251-259 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that the Boltzmann equation with no loss term cannot have a global solution when the mean free path is small, even with initial data describing a cloud of gas released in an infinite vacuum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090120
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