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  • Mathematics and Statistics  (705)
  • Wiley-Blackwell  (705)
  • Periodicals Archive Online (PAO)
  • Annual Reviews
  • 1990-1994  (520)
  • 1980-1984  (185)
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  • Wiley-Blackwell  (705)
  • Periodicals Archive Online (PAO)
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  • 1
    Electronic Resource
    Electronic Resource
    Local validity of the boltzmann equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 539-549 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The validity of the Boltzmann equation is proved, locally in time, by showing that its solution is a limit of solutions of the BBGKY hierarchy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060135
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  • 2
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    Masthead (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130601
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  • 3
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    Non-homogeneous non-linear damped wave equations in unbounded domainsSupported by the SFB 256 of the Deutsche Forschungsgemeinschaft at the University of Bonn, F.R.G. (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 481-491 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a global existence theorem for solutions of utt - ∂iaik (x)∂ku + ut = ƒ(t, x, u, ut, ∇u, ∇ut, ∇2u), u(t = 0) = u0, ut(=0)=u1, u(t, x), t ⋝ 0, x∊Ω.Ω equals ∝3 or Ω is an exterior domain in ∝3 with smoothly bounded star-shaped complement. In the latter case the boundary condition u|∂Ω = 0 will be studied. The main theorem is obtained for small data (u0, u1) under certain conditions on the coefficients aik.The Lp - Lq decay rates of solutions of the linearized problem, based on a previously introduced generalized eigenfunction expansion ansatz, are used to derive the necessary a priori estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130604
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  • 4
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    Non-linear flexings in a periodically forced floating beam (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 1-33 
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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 considers periodic flexing in a floating beam, in the presence of a small periodic forcing term. The beam is considered as a vibrating beam with the free-end boundary condition, in the presence of an additional restoring force due to flotation, which becomes zero as soon as the beam lifts out of the water. The equation is therefore non-linear. A theorem is proved which shows that in the presence of small periodic forcing terms, both small- and large-amplitude solutions can exist. Numerical evidence is presented, which shows that the large-amplitude solutions are stable over a wide range of frequency and amplitude, and suggests a cusp-like surface for the multiple solutions.
    Additional Material: 24 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670140102
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  • 5
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    A half-space problem for a non-linear Boltzmann equation arising in semiconductor statistics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 121-137 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In semiconductors the distributions of electrons satisfy a non-linear Boltzmann-Vlasov equation. We consider the half-space problem arising in the study of boundary layers when the mean free path tends to zero. We prove the existence and the uniqueness of the solution for any prescribed entering distribution. We establish that this solution tends towards a Fermi-Dirac distribution exponentially fast.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140204
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  • 6
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    Global existence of weak solutions for a system of non-linear Boltzmann equations in semiconductor physics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 139-153 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we give a proof of the global existence of weak solutions for the semiconductor Boltzmann equation. This equation rules the evolution of the distribution function of carriers in the kinetic model of semiconductors. The main tool for the proof consists of a recent compactness result on velocity averages of solutions of transport equations. This result needs a L2-estimate of the electric field, which is obtained from the energy estimate, using the original regularization procedure of the problem, proposed in this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140205
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  • 7
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    An artificial boundary condition for an advection-diffusion equation (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 155-175 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Consider the advection-diffusion equation: u1 + aux1 - vδu = 0 in ∝n × ∝+ with initial data u0; the Support of u0 is contained in ∝-n(x1 〈 0) and a: ∝n → ∝ is positive. In order to approximate the full space solution by the solution of a problem in ∝-n × ∝+, we propose the artificial boundary condition: u1 + aux1 = 0 on ∑. We study this by means of a transmission problem: the error is an O(v2) for small values of the viscosity v.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670140302
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  • 8
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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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.1670140401
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  • 9
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    On the linear piezoelectricity of composite materials (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 403-412 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: From the equations of the linear piezoelectricity for a composite material with a periodic structure we derive the dynamical solution by means of Bloch expansion techniques. This expression techniques. This expression allows, as a limit case, a comparison with the homogenization method, and the macroscopic coefficients are also deduced.
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    URL: http://dx.doi.org/10.1002/mma.1670140604
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  • 10
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    The double-layer potential operator over polyhedral domains II: Spline Galerkin methods (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 23-37 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We examine the numerical approximation of the integral equation (λ - K)u =f, where K is the double layer (harmonic) potential operator on a closed polyhedral surface in ∝3 and λ, ∣λ∣≥1, is a complex constant. The solution is approximated by Galerkin's method, which is based on piecewise polynomials of arbitrary degree on graded triangulations. By utilizing spline spaces which are modified in that the trial functions vanish on some of the triangles closest to the vertices and edges, we investigate the stability of this method in L2. Furthermore, the use of suitably graded meshes leads to the same quasioptimal error estimates as in the case of a smooth surface.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670150104
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  • 11
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    Time delay and finite differences for the non-stationary non-linear Navier-Stokes equations (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 89-108 
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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 present paper we use a time delay ∊ 〉 0 for an energy conserving approximation of the non-linear term of the non-stationary Navier-Stokes equations. We prove that the corresponding initial-value problem (N∊) in smoothly bounded domains G ⊆ ∝3 is well-posed. We study a semidiscretized difference scheme for (N∊) and prove convergence to optimal order in the Sobolev space H2(G). Passing to the limit ∊→0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier-Stokes problem (No) in a weak sense (Hopf).
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    URL: http://dx.doi.org/10.1002/mma.1670150204
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  • 12
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    On a free-boundary problem arising in the study of flame propagation (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 479-493 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of a weak solution of a two-dimensional non-stationary free-boundary problem related to flame propagation is established. The main feature of the problem is that the nonlinear coupling of the two parabolic equations occur on the free boundary and has exponential growth.
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    URL: http://dx.doi.org/10.1002/mma.1670150704
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  • 13
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    On the fundamental solutions of the operators of S. Timoshenko and R. D. Mindlin (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 525-535 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Our recent paper about some new fundamental solutions is complemented by a representation of the fundamental solution of certain evolution operators of fourth order in terms of a family of fundamental solutions of operators of second order. By applying this to the operators of vibrating beams and plates we deduce representations of their fundamental solutions as simple definite integrals over tabulated functions.
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    URL: http://dx.doi.org/10.1002/mma.1670150802
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  • 14
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    On the determination of the worst sampling error in a communication system for pulse-amplitude-modulated signals. I: The general model (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 511-523 
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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 a mathematical model of a communication system perturbed by statistical sampling errors (timing jitter). The aim is to find an ‘optimal’ impulse response for the system, the optimization problem actually being a minimax problem. that is we put the model into a game-theoretical framework. The basic game turns out to be a statistical game similar to those arising from estimation problems in statistics.Earlier results concerning least-favourable sampling error distributions published by Krabs and Vogel are supplemented by estimations of the number of support points of the least-favourable distribution.Furthermore, we state the existence of the saddle points of our game, which formerly has only been proved for some special cases. In the first part we treat the general situation, where one strategy set for the game - the set of all feasible impulse responses - forms a vector space with infinite dimension. In the second part we discuss the problem in the case that the impulse responses are restricted to a finite-dimensional subspace of the whole infinite-dimensional subspace.
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    URL: http://dx.doi.org/10.1002/mma.1670150706
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  • 15
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    Regularization of a non-characteristic Cauchy problem for the heat equation (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 537-545 
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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-characteristic Cauchy problem for the heat equation uxx(x,t) = u1(x,t), 0 ≤ x ≤ 1, - ∞ 〈 t 〈 ∞, u(0,t) = ϕ(t), ux(0, t) = ψ(t), - ∞ 〈 t 〈 ∞ is regularizèd when approximate expressions for ϕ and ψ are given. Properties of the exact solution are used to obtain an explicit stability estimate.
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    URL: http://dx.doi.org/10.1002/mma.1670150803
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  • 16
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    Masthead (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992) 
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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.1670150901
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  • 17
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    Inhomogeneous Timoshenko beam equationsThis is the text of a short communication given by the first author at the 5th Symposium on ‘Control of distributed parameter systems’ held at Perpignan, France, in June 1989. (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 621-630 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The so-called Timoshenko beam equation is a good linear model for the transverse vibrations of a homogeneous beam. Following the variational approach of Washizu, the governing equation is deduced in the case when the physical/geometrical parameters of the beam vary along its axis. The equation may not be studied by means of the iterated use of Fourier series. However, a convenient change of variables permits us to prove the well-posedness of the associated Cauchy problem for a beam with sliding ends (the solution is intended in a mild sense). The proof is given in an abstract framework.
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    URL: http://dx.doi.org/10.1002/mma.1670150903
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  • 18
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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.1670160101
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  • 19
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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.
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    URL: http://dx.doi.org/10.1002/mma.1670160104
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  • 20
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670160105
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  • 21
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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.
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    URL: http://dx.doi.org/10.1002/mma.1670160202
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  • 22
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    Decay properties of periodic, radially symmetric solutions of Sine-Gordon-type equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 359-378 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the radially symmetric, nonlinear wave equation and discuss the asymptotic behaviour as r → ∞ of solutions which are T-periodic in time t. It is shown that only two possibilities of decay can arise, namely polynomial like t-½(n-1) and exponential e-bt for some b 〉 0. Existence results are obtained.
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    URL: http://dx.doi.org/10.1002/mma.1670160504
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  • 23
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The three-dimensional interface problem with the homogeneous Lamé system in an unbounded exterior domain and holonomic material behaviour in a bounded interior Lipschitz domain is considered. Existence and uniqueness of solutions of the interface problem are obtained rewriting the exterior problem in terms of boundary integral operators following the symmetric coupling procedure.The numerical approximation of the solutions consists in coupling of the boundary element method (BEM) and the finite element method (FEM). A Céa-like error estimate is presented for the discrete solutions of the numerical procedure proving its convergence.
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    URL: http://dx.doi.org/10.1002/mma.1670161105
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  • 24
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    Gradient bounds for plasma confinement (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 68-72 
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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 plasma confinement in a Tokomak machine has recently attracted considerable mathematical attention. In the present article, gradient bounds for the solution are obtained through the use of differential inequalities and the Hopf maximum principle. These estimates, which take slightly different forms in the plasma and vacuum regions, become exact in the one-dimensional case. An estimate is also given for the distance from the boundary of the interior point where the maximum of the solution is attained.
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    URL: http://dx.doi.org/10.1002/mma.1670020107
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  • 25
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    Differentiable dependence upon the data in a one-phase Stefan problem (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 73-90 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is well known that the free boundary of the one-phase Stefan problem (1.1-5) depends continuously on the boundary data [1]. In this paper we prove that, in addition, the solution operator S which, to each g. assigns the corresponding free boundary, is continuously Frechet differentiable and we give the defining formulas of the Frechet derivative.
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    URL: http://dx.doi.org/10.1002/mma.1670020108
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    A singular perturbation approach for a reaction diffusion system arising in nuclear reactor theory (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 91-107 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The qualitative behavior of the solutions of a reaction-diffusion system arising in the theory of nuclear reactors is investigated by means of singular perturbation techniques, the small parameter ∊ representing the inverse of neutron velocity. At the lowest approximation for small ∊ the solutions exhibit oscillations about the unique strictly positive equilibrium, much as in the case of the associated lumped parameter system. A two-times representation for solutions of small amplitudes is also given.
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    URL: http://dx.doi.org/10.1002/mma.1670020109
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  • 27
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    Masthead (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980) 
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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.1670020201
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  • 28
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    The effect of a thin inclusion of high rigidity in an elastic body (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 251-270 
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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 an elastic body comprising an inclusion whose thickness is 2∊ and for which Lamé's constants are λ∊ and μ. We are interested in the limit behaviour of the inclusion, when ∊ → 0 and μ∊ → ∊; that is when the inclusion becomes thiner and more rigid. Different behaviours are possible, according to the rate at which μ∊ converges to infinity; the limit inclusion may “vanish” if it is not very rigid, but also it may be entirely solid.
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  • 29
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    Scattering of elastic waves through a heterogeneous medium (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 271-287 
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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 the elastic wave diffraction in R3 through a heterogeneous medium, with periodic structure, which occupies a bounded domain. We show that, as the period tends to zero, the solution tends, in some sense, to the solution corresponding to the diffraction by an obstacle made of the classical “homogenized medium”. An analogous result is also proved for the scattering frequencies and the associated scattering functions.
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    URL: http://dx.doi.org/10.1002/mma.1670020303
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    Partition of energy in strongly damped generalized wave equations (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 95-103 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Dissipative perturbations of hyperbolic equations such as utt + But + A2u = 0 with positive operators A, B are considered. The rates of decay and partition of energy theorems are established for solutions of these equations.
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    A free boundary problem and stability for the rectangular plate (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 129-138 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In the recent paper [13] we have answered the question of stability for the linear circular plate which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. In this case there are radially symmetric solutions and the contact region is a disk of a smaller radius. This simplified the determination of the critical parameter values for which the plane jumps to another state. For the rectangular plate continuation has to be applied to the variational inequality in order to determine the contact region and evalute the stability criterion. A numerical method is developed for a discretization of the problem and is used to compute the critical load both in the simply supported and the clamped case.
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    Global solutions of Yang-Mills-Higgs systems on four-dimensional Minkowski space: I. Existence (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 153-165 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of global solutions to the Cauchy problem for Yang-Mills-Higgs systems in the temporal gauge is examined. The results apply to the self-coupling of the Higgs field. Results from other works are strengthened.
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    On the construction of minimizing sequences for convex functionals with upper and lower bounding functionals (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 189-199 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method is described for constructing upper and lower bounds for the stationary values of a general class of convex functionals. The method relies of the existence of approximating convex functionals whose Gâteaux derivatives are presumed to have simpler structure than the original. The method is iterative in that convergent sequences of bounds can be constructed. Some applications to the Laplacian operator are included.
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    Randwertaufgaben in der verallgemeinerten Potentialtheorie (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 218-228 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The Neumann and Dirichlet boundary value problem of generalized potential theory is considered. Based on a compact imbedding result, existence and uniqueness theorems are obtained for Riemannian manifolds with compact boundary (‘interior and exterior domains’).
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    A constructive method for solving the displacement boundary-value problem of elastostatics by use of global basis systemsDedicated to Claus Müller on the occasion of his 70th birthday. (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 105-128 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we are concerned with the three-dimensional homogeneous isotropic elastostatic boundary-value problem. Global basis vector fields are shown to be constructive structures for approximating the solution. The theoretical tool is a regularity condition developed from the classical integral equation approach. The paper ends with some reflections on the practical computability and numerical applicability.
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    Linear stability condition for explicit Runge-Kutta methods to solve the compressible Navier-Stokes equations (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 139-151 
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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: A linear stability condition is dervied for explicit Runge-Kutta methods to solve the compressible Navier-Stokes equations by central second-order finite-difference and finite-volume methods. The equations in non-conservative form are simplified to quasilinear form, and the eigenvalues of the resulting coefficient matrices are determined for general co-ordinates. Assuming a well-posed Cauchy problem with constant coefficients, the von Neumann stability analysis yields sufficient stability conditions for viscous-inviscid operator-splitting schemes. They have been applied in computational aerodynamics to solve the compressible Navier-Stokes equations by an unsplit explicit Runge-Kutta finite-volume method.
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    Global solutions of Yang-Mills-Higgs systems on four-dimensional Minkowski space: II. Some properties of solutions (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 167-176 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper concerns the properties of global solutions to the Cauchy problem of Yang-Mills-Higgs systems in the temporal gauge. The following properties are considered: global analyticity of solutions, an approximation property, conservation of the topological class of solutions, scattering of a part of the energy of solutions through a light cone.
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    Examples of embedded eigenvalues for the Dirichlet-Laplacian in domains with infinite boundaries (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 177-182 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: For certain unbounded domains the Laplace operator with Dirichlet condition is shown to have an unbounded sequence of eigenvalues which are embedded into the essential spectrum. A typical example of such a domain is a locally perturbed cylinder with circular cross-section whose diameter in some bounded subset is greater than at infinity.
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    The propagation problem and far-field patterns in a stratified finite-depth ocean (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 199-208 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper we investigate the direct problem associated with the scattering of ‘plane waves’ from an object submerged in an ocean of finite depth. An integral representation for the Dirichlet problem is found, from which a formula for the far-field pattern evolves.A density theorem is established concerning the set of all far-field patterns. This theorem is essential for the reconstruction of the submerged object, the ‘inverse’ problem [2], [4], [5].
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    Solution of a class of partial differential equations. Some diffusion equations (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 221-228 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this article we present the solution of linear partial differential equations of the form ∂tf = L̂f, for initial value problems. Also the solution of some diffusion equations will be discussed.
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    Über das asymptotische Verhalten thermoelastischer Wellen im R3Diese Arbeit entstand mit Unterstützung des durch die Deutsche Forschungsgemeinschaft getragenen Sonderforschungsbereiches 72 an der Universität Bonn. (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 312-317 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In [L] the author provided existence theorems for initial-boundary-value problems in thermoelasticity for unbounded domains. Continuing this work the asymptotic behaviour of solutions in R3 with respect to t → ∞ will be described in this paper.
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    Local energy decay of solutions of linearized shallow-water equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 318-327 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We prove the local decay of the energy of the solution to a mixed initial boundary value problem for the linearized shallow-water equations with constant coefficients, where the domain is a half-plane, a certain dissipative boundary condition is prescribed and the initial data have compact support contained in the open half-plane.
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    A solution to the equations of shell theory (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 341-363 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: In this paper the Vekua-Dikmen formulation of the equations of shell theory as a heirarchy are presented as a hypercomplex system. Using the function theory associated with this algebra the torsion problem is solved as an integral representation.
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    Finite element approximation of vector fields given by curl and divergence (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 328-335 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a finite element approximation scheme for the system curl is considered. The use of pointwise approximation of the boundary condition leads to a nonconforming method. The error estimate is proved and numerically tested.
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    Condition number of matrices derived from two classes of integral equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 364-392 
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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 investigate some integral equations, i. a. the so-called Kupradze functional equations, where the two variables of the kernel belong to two different point sets. An extensive survey of the literature shows the various applications of these equations.By a discretization of the integral equations they are replaced by systems of linear algebraic equations. The condition number of the corresponding matrices is investigated, analytically and numerically. It is thereby quantitatively found in which way the condition of the matrices deteriorates when the two point sets are moved away from each other.
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    Mathematische Behandlung ernes Modells der Haemodialyse (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 393-404 
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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 simple mathematical model for the process of hemodialysis is presented. This model is based on a system of two linear differential equations of first order with partly discontinuous coefficients that describe the time-development of the concentrations of a certain toxin (like urea) in the intra- and extracellular part of the human body. The main result is the existence of periodic positive solutions of this system under the natural assumption that the generation of the toxin and its removal by hemodialysis are periodic processes. These periodic positive solutions are also computed numerically for a realistic choice of the coefficients of the modelling differential equations.
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    Global weak solutions to the problem of continuous sedimentation of an ideal suspension (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 1-22 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present the sedimentation of an ideal suspension in a continuous thickener as an initial value problem and study the transient states by constructing the corresponding global weak solutions. Finally, we obtain a way to control the operation of the thickener.
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    An existence theorem for Poiseuille flow with surface tension in an open channel (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 23-30 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Poiseuille-type flow in an open channel is studied taking surface tension and wall adhesion into account. A proof is presented of the existence of a solution under certain conditions.
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    On the convexity of equilibrium plasma configurations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 435-443 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We investigate the problem of plasma confinement by a magnetic field in an infinite cylinder. We show that if the cylinder has convex cross-section, then there exists an equilibrium plasma configuration with convex cross-section.
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    On the Vlasov hierarchy (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 445-455 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Motivated by a recent paper of H. Narnhofer and G. Sewell, we investigate the problem of existence and uniqueness of solutions of the Vlasov hierarchy. It is shown that the unique solution of the Vlasow hierarchy is induced by the flow on the space of probability measures on R6 which is obtained from the solution of the Vlasov equation.
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    A study of a non-linear kinetic model for an ionized gas (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 95-109 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: A non-linear one-dimensional kinetic model for an ionized gas is considered. In this model the collisions between charged and neutral particies and the field generated by the charges are taken into account. The Cauchy problem for the resulting system of equations is examined. An existence and uniqueness theorem of a global in time solution is proved.
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    Asymptotic analysis of the quantum Liouville equation (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 143-157 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We present an asymptotic analysis of the quantum Liouville equation with respect to the Planck's constant, which models the temporal evolution of the (quasi)distribution of an ensemble of electrons under the action of a potential. We consider two cases: firstly a smooth potential, and secondly a potential modelled by a δ-distribution. In both cases the zeroth-order term behaves classically. In the smooth case the classical Liouville equation is satisfied and in the case for the δ-potential an interface condition is derived, so that everything is reflected at the potential barrier.
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    A two-species plasma in the limit of large ion mass (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 159-167 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Classical solutions of the relativistic Vlasov-Maxwell system are considered, describing a collisionless plasma with two species of particles. ions and electrons. It is shown that as the ion mass m tends to infinity, the corresponding solution of the relativistic Vlasov-Maxwell system tends to the solution of a system, in which the ions are given by a fixed ion background and only the electrons move. The convergence is uniform on compact time intervals, with an asymptotic convergence rate of m-1.
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    Stability and instability of the energy dependent diffusion system in reactor dynamics (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 488-505 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The purpose of this paper is to give a systematic analysis for the linear energy dependent diffusion system in reactor dynamics, taking into consideration of delayed neutrons. This analysis includes the existence of a unique positive solution for the time dependent system, the asymptotic behaviour of the solution as t → ∞, the stability and instability of steady-state solutions, and the existence and uniqueness of a steady-state solution for the time-independent system. Using the notion of upper and lower solution, we establish some threshold conditions for insuring the asymptotic behaviour of the solution and the stability and the instability of any given unperturbed solution, including steady-state solution. In fact, these conditions characterize the stability and the instability property of the solution, and yield a bifurcation result in terms of either the size of the diffusion domain or the physical parameters of the diffusion medium. We also discuss the case without the effect of delayed neutrons.
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    Approximation of the scattering state by means of the radiation boundary condition (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 506-515 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The approximation sequence for the scattering state is constructed by the solutions for the reduced wave equations in some bounded domains with radiation conditions at their boundary. The corresponding discrete approximation is also considered by the Bubnov-Galerkin method.
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    Partial asymptotic stability via limiting equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 516-522 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper the limiting equations approach is applied to study the stability properties with respect to a part of the state variables for nonautonomous dynamical systems. Sufficient conditions are given for uniform asymptotic eventual strongly partial stability and for uniform asymptotic partial stability. An application of the results is given.
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    The kinetics equations in a multiplying medium with free boundaries (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 263-272 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: We study a mathematical model of neutron multiplication in a slab S, by taking into account temperature feedback effects and considering one group of delayed neutrons. The thickness 2a of S is time dependent because of temperature variations due to the energy released by fissions.Starting from a quite detailed picture of the physical phenomena occurring in S, we derive a system of three coupled ordinary differential equations for the total number of neutrons F̂ = F̂(t), for the total number of precursors Ĉ = Ĉ(t), and for the half-thickness of S, a = a(t).We finally examine some stability properties of such a system of ordinary differential equations.
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    Dissipative Maxwell's equations at low frequencies (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 305-322 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A study of the low-frequency behaviour of solutions to dissipative Maxwell's equations with discontinuous coefficients is given.
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    On spherical spline interpolation and approximation (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 551-575 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Spherical spline functions are introduced by use of Green's surface functions with respect to the (Laplace-)Beltrami operator of the (unit) sphere. Natural (spherical) spline functions are used to interpolate data discretely given on the sphere. A method is presented that allows the smoothing of irregularities in measured values or experimental data. Extensions of Peano's theorem and Sard's theory of best approximation to the spherical case are given by integral formulas. Schoenberg's theorem is transcribed into spherical nomenclature.
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    Masthead (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990) 
    Details
    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.1670130501
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    An optimal control problem for the Helmholtz equation in a stratified Shallow oceanThis research was supported in part by the U.S. AFOSR86-0269. (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 405-419 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we shall consider a kind of optimal control of the Robin problem. First, we discuss the solvability of the Robin problem, which is not uniquely solvable in general. Then we find the representation of the far-field pattern in terms of the minimal solution to an integral equation. Based on this representation, an optimization problem is discussed and a Galerkin scheme for the solution is presented.
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    Higher moments for kinetic equations: The Vlasov-Poisson and Fokker-Planck cases (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 441-452 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let us consider a solution f(x,v,t)∊L1(∝2N × [0,T]) of the kinetic equation where |v|α+1 fo,|v|α ∊L1 (∝2N × [0, T]) for some α〈 0. We prove that f has a higher moment than what is expected. Namely, for any bounded set Kx, we haveWe use this result to improve the regularity of the local density ρ(x,t) = ∫ƒdν for the Vlasov-Poisson equation, which corresponds to g = Eƒ, where E is the force field created by the repartition ƒ itself. We also apply this to the Bhatnagar-Gross-;Krook model with an external force, and we prove that the solution of the Fokker-Pianck equation with a source term in L2 belongs to L2([0, T]; H1/2(∝x,v2N)).
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    On the mathematical foundations of hyperthermia therapy (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 467-479 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Hyperthermia is an aid to standard cancer therapy. The aim is to heat up a tumour region inside the patient's body with the help of microwave radiation. The microwayes are generated by some suitable antenna array. Here we investigate the control properties of such antenna configurations and determine their resolution capabilities. We will define the hyperthermia operator, which can produce every field of any antenna array up to any degree of accuracy. We shall see that this operator is compact and we are able to compute a singular system under general assumptions explicitly. This, together with a detailed knowledge of the decay of the singular values, constitutes the tools with which we treat the previously stated problems. We examine the propagation of microwave radiation in homogeneous media and then carry over the results obtained to the case of inhomogeneous media.
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    An improved boundary element method for the charge density of a thin electrified plate in ∝3 (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 291-303 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A weakly singular integral equation of the first kind on a plane surface piece Γ is solved approximately via the Galerkin method. The determination of the solution of this integral equation (with the single-layer potential) is a classical problem in physics, since its solution represents the charge density of a thin, electrified plate Γ loaded with some given potential. Using piecewise constant or piecewise bilinear boundary elements we derive asymptotic estimates for the Galerkin error in the energy norm and analyse the effect of graded meshes. Estimates in lower order Sobolev norms are obtained via the Aubin-Nitsche trick. We describe in detail the numerical implementation of the Galerkin method with both piecewise-constant and piecewise-linear boundary elements. Numerical experiments show experimental rates of convergence that confirm our theoretical, asymptotic results.
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    On the uniqueness of motion of viscous gaseous stars (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 391-404 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The existence of solutions of the evolutionary equations of motion of a star regarded as a compressible viscous fluid with self-gravitation, bounded by a free surface, has recently been considered [3, 4]. In this paper I study the uniqueness of the above solutions.
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    The initial boundary value problem for the Schröudinger equation (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 385-390 
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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 study the stability properties of the one-dimensional Schrödinger equation with boundary conditions that involve the derivative in the direction of propagation (or time). We show that this type of boundary condition might cause a strong growth of the amplitude of the solution. Such a model is not useful for numerical computations. One example is the parabolic wave equation in underwater acoustics for wave propagation in a downsloping duct with the normal derivative condition ∂u/∂n =0 at the bottom.
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    Continuous dependence on the heat source and non-linear stability for convection with internal heat generation (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 373-383 
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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: It is shown that the solution to the boundary-initial value problem for a heat-conducting viscous fluid depends continuously on changes in the heat supply function, for the improperly posed backward in time problem. A non-linear convection threshold is also determined for the problem of a layer of fluid heated internally (non-uniformly), with zero neat flux on the lower boundary and constant-temperature upper surface.
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    An asymptotic-numerical approach to the coronal loop problem (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 431-439 
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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 coronal loop problem is characterized by mixed boundary conditions and the loop length condition, which is global. Using singular perturbation methods one can identify and construct two boundary layers at the base of the loop.Extending this to a combined asymptotic-numerical treatment it is possible to construct two static solutions satisfying the same conditions; this unusual feature arises from the presence of the first boundary layer, which corresponds with a steep temperature gradient and an energy balance dominated by conduction and radiation losses.
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    Determination of an unknown function in a parabolic equation with an overspecified conditionThis work was funded by NSERC Canada. (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 421-430 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the inverse problems of identifying some space-dependent unknown coefficients in parabolic equations subject to initial boundary value conditions along with an overspecified condition at the final time t = T. We use the overspecified information to transform the problems into non-linear parabolic equations involving a functional of the solution with respect to the time variable. This transformation allows us to establish existence theorems for these inverse problems by employing the Schauder fixed-point theorem.
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    Advective estimates (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 453-465 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Consider the partial differential equation: wt + bw + a· ∇w = g in ∝n × [0, T] (x1 〈0) and if the function a1 is positive, then, in the left half-space, the solution w is an O (ν) for small Viscosity ν.
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    Asymptotic expansions for hyperbolic-parabolic systems with a small parameter (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 493-514 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper we consider initial-boundary value problems for systems with a small parameter ∊. The problems are mixed hyperbolic-parabolic when ∊ 〉 0 and hyperbolic when ∊ = 0. Often the solution can be expanded asymptotically in ∊ and to first approximation it consists of the solution of the corresponding hyperbolic problem and a boundary layer part. We prove sufficient conditions for the expansion to exist and give estimates of the remainder. We also examine how the boundary conditions should be choosen to avoid O(1) boundary layers.
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/mma.1670140201
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    The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 35-61 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We prove the existence of a unique, global classical solution of the quantum Vlasov-Poisson problem posed on the phase space ∝x3 × ∝v3. The proof is based on a reformulation of the quantum Vlasov-Poisson problem as a system of countably many Schrödinger equations coupled to a Poisson equation for the potential. The Schrödinger-Poisson problem is first analysed on a bounded domain in ∝x3 and the solution of the whole-space problem is then obtained by a limiting procedure in which the domains ‘tend’ to ∝x3.
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    Dynamical shape control and the stabilization of non-linear thin rods (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 63-78 
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    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 problem of stabilizing the motion of the tip of a thin rod by controlling the shape of the rod, that is its length, dynamically. Well-posedness of the associated state equations, valid on a moving domain, is proved, and the necessary conditions of optimality for the control problem are derived. The theory applies to materials where the stress-strain relation is both non-linear and non monotone, so that hysteresis effects arising from solid-solid phase transitions in the rod are included.
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    URL: http://dx.doi.org/10.1002/mma.1670140104
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    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670140301
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    Entropy compactification in Lagrangean gas dynamics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 207-216 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    An approximation of the thermal field in a continuous casting process of a thin metal layer (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 217-226 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the problem of a phase change in a continuous casting process: molten bronze is poured on to a moving steel strip cooled from below, in order to solidify the bronze. An estimate of the width of the solidification zone, depending on the thickness of the strip and on the casting velocity, is obtained, neglecting conduction in the direction of the strip motion.
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    Differential stability of solutions to parametric optimization problems (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 281-294 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A method for the differential stability of solutions to a class of solutions to a class of parametric optimization problem is prposed. Any solution of the parametric optimization problem is given as a fixed point of the metric projection onto the set of admissible coefficients. A new result on the differential stability of the metric projection in Sobolev space H2(Ω)onto a set of admissible parameters is obtained. The stability results with respect to perturbations of observations for the solutions to a coefficient estimation problem for a second-order elliptic equation are derived.
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    Charge transport in semiconductors with degeneracy effects (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 301-318 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It has been a common procedure to derive a model for charge transport in degenerate semiconductor material by incorporating a Fermi-Dirac distribution into the classical drift-diffusion model. In this work a Boltzmann equation with a non-linear collision term is considered. A new fluid dynamical model is derived by considering small perturbations of the thermal equilibrium. The analysis contains an existence and uniqueness proof for the Boltzmann equation, a justification of the perturbation argument and a study of initial boundary value problems for the new fluid dynamical model.
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    On the theory of cylindrical resonators (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 355-375 
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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 contains an introduction to the methods of operator-valued functions for solving some non-linear eigenvalue problems of the electrodynamics of guided waves. One simple example of the problem of fundamental frequencies for the rectangular-slot resonator is considered that gives an opportunity to follow all the steps and features of this technique.
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    Diffraction by an acoustically transmissive or an electromagnetically dielectric half-plane (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 387-402 
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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 gives a mathematical model for an acoustically penetrable or electromagnetically dielectric half-plane. An approximate boundary condition is used that depends on the thickness of, and the material constants for, the half-plane. A solution is obtained, by using the approximate boundary condition, for the problem of a line source field diffracted by a penetrable/dielectric half-plane. The asymmetry of the approximate boundary condition results in a matrix Wiener-Hopf problem, which is solved explicitly.
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    Time decay of solutions of semilinear strongly damped generalized wave equations (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 427-443 
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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 asymptotic behaviour in time of the solutions of dissipative perturbations of wave-type equations in ∝N, utt + But + Au + G(u) = 0, with commuting positive operators A, B and a power like non-linearity G(u). First we give some (pseudo) conformal invariants of the linear operator in the equation. This allows us to derive optimal decay rates for the solutions of the linearized problems. We then prove some decay estimates for the non-linear problems using the tools of scattering theory and the aforementioned conformal invariants.
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    A trace theorem for solutions of linear partial differential equations (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 553-562 
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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 a trace regularity theorem for the solutions of general linear partial differential equations with smooth coefficients. Our result shows that by imposing additional microlocal smoothness along certain directions, the trace of the solution on a codimension-one hypersuface will be just as regular as the solution itself. The proof is based on the Hörmander-Nirenberg pseudo-differential cut-off technique and a ‘fattening’ lemma, together with standard energy estimates.
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    Convergence analysis for a multiplicatively relaxed EM algorithm (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 573-593 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The expectation maximization (EM) algorithm is an iterative procedure used to determine maximum likelihood estimators in situations of incomplete data. In the case of independent Poisson variables it converges to a solution of a problem of the form min ∑[〈ai,x〉 - bi log 〈ai, x〉] such that x ≥0. Thus, it can be used to solve systems of the form Ax = b, x≥0 (with A stochastic and b positive.) It converges to a feasible solution if it exists and to an approximate one otherwise (the one that minimizes d (b, Ax), where d is the Kullback-Leibler information divergence). We study the convergence of the multiplicatively relaxed version proposed by Tanaka for use in positron emission tomography. We prove global convergence in the underrelaxed and unrelaxed cases. In the overrelaxed case we present a local convergence theorem together with two partial global results: the sequence generated by the algorithm is bounded and, if it converges, its limit point is a solution of the aforementioned problem.
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    Solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $$\end{document}. Exact solutions of some partial differential equations in mechanics and physics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 615-631 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: The solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $\end{document}, for L̂ a linear operator are derived. Different forms for L̂ whether it is time independent or time dependent and self-commutative (or not) at different times are considered separately. By using the results obtained, exact solutions of some partial differential equations are found for the first time.
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    Ein nichtlineares Glättungsverfahren zur rekonstruktion von flugbahnen aus radardaten (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 497-509 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Data processing is an important tool in airspace surveillance and air traffic control today. In this paper the problem is treated how to reconstruct a flown trajectory from its correlated radar plots subject to a certain knowledge of the aircraft manoeuverability and the radar measurement statistics. A variational approach leads to a generalized smoothing spline method. Simulation results are presented.
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    Über die existenz und eindeutigkeit einer lösung für ein randwertproblem für eine gleichung vom gemischten typ in einem rechteck (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 510-528 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the paper a boundary value problem is studied for the equation of mixed typek(y)uxx + uyy + r(x, y)u = f(x, y) in the rectangular domain {(x, y)| -1 〈 x 〈 +1, yc 〈 y 〈 yH} with yc 〈 0, yH 〉 0, k(y) = sign y|y|m, m 〉 0 (and more generally for a function k = k(y) with k(O) = 0, k(y)y 〉 O for y ≠ O). Specific for the stated problem is that no data are prescribed on the line {(x, yc), -1 〈 x 〈 +1}. It is proved that the formulated problem is well-posed in the sense that there is at most one quasi-regular solution and that a generalized solution exists. The energy-integral-(abc-)method is used to show uniqueness and to obtain an apriori estimate for the solution of the adjoint problem whence the existence statement follows.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040133
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    Masthead (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670150201
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    Masthead (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670150301
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    On the moving Preisach model (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 145-157 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that the moving model, which is a variant of the Preisach model for hysteresis, possesses the wiping out property and is continuous in C[0, T] under natural assumptions.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670150302
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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
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1002/mma.1670160103
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    Low Reynolds number deformation of compound drops in shear flow (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 61-74 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160106
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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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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160203
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    Radially symmetric global classical solutions of non-linear wave equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 131-149 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Cauchy problem for semilinear wave equations utt - Δu + h(|x|)up = 0 with radially symmetric smooth ‘large’ data has a unique global classical solution in arbitrary space dimensions if h is non-negative and p any odd integer provided the smooth factor h vanishes with sufficiently high order at the origin and is bounded together with its derivatives.
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    URL: http://dx.doi.org/10.1002/mma.1670160206
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    The sommerfeld half-plane problem revisited, II the factoring of a matrix of analytic functionsThese results were announced at the XXth General Assembly of the U.R.S.I. held in Washington, D.C., August 1981. (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 14-21 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A half-plane under plane wave excitation obeys a Dirichlet boundary condition on one side and a Neumann boundary condition on the other. These boundary conditions contrast the ones used by A. Sommerfeld in his classical paper. The present problem leads to a system of integral equations of the Wiener-Hopf type which may be solved by a matrix factoring method suggested by A. E. Heins in 1950.
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    URL: http://dx.doi.org/10.1002/mma.1670050103
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    Wave equations with time-dependent spatial operators of higher order (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 453-468 
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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 initial-boundary value problem for ∂t2u(t,x)+A(t)u(t,x)+B(t)∂tu(t,x)=f(t,x) on [0,T]×Ω(Ω⊂∝n) with a homogeneous Dirichlet boundary condition; here A(t) denotes a family of uniformly strongly elliptic operators of order 2m, B(t) denotes a family of spatial differential operators of order less than or equal to m, and u is a scalar function. We prove the existence of a unique strong solution u. Furthermore, an energy estimate for u is given.
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    URL: http://dx.doi.org/10.1002/mma.1670150702
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    On degenerate diffusion with very strong absorption (1992)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 15 (1992), S. 469-477 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the existence of weak global solutions to the degenerate diffusion equation (1) with singular absorption term. Moreover we investigate the regularity up to the quenching time and we show by means of explicit solutions that our regularity results are optimal.
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    URL: http://dx.doi.org/10.1002/mma.1670150703
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    A non-isentropic Euler-Poisson model for a collisionless plasma (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 409-442 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We analyse transonic solutions of the one-dimensional Euler-Poisson model for a collisionless gas of charged particles in the non-isentropic steady-state case. The model consists of the conservation of mass, momentum and energy equations. The electric field is modelled self-consistently (Coulomb field). Boundary conditions on the particle density and particle temperature are imposed.The analysis is based on representing solutions piecewise as orbits in the particle-density-electric-field phase plane and connecting the orbit segments by the jump and entropy conditions.We characterize the set of all solutions of the Euler-Poisson problem. In particular, we show that, depending upon the length of the interval on which the boundary value problem is posed, fully subsonic, one-shock and (in certain cases) two-shock transonic and smooth transonic solutions exist. Also, numerical computations illustrating the structure of the solutions are reported.
    Additional Material: 21 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160603
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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.1670160801
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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 
    Details
    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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