Asymptotic Analysis - Volume 23, issue 3-4

Authors: Langlois, A. | Marion, M.

Article Type: Research Article

Abstract: This paper is concerned with the thermal diffusional model borrowed from the theory of combustion. The analytic methods currently used to investigate this model require a near‐equidiffusion condition, the inverse of the activation energy being the small parameter. The first step in these methods consists in assuming a suitable bound on the temperature. The aim of this paper is to derive rigorously such a bound. We show that the temperature is bounded independently of the activation energy β uniformly in time, at least for sufficiently large values of β. The proof relies on the use of a Lyapunov function …first introduced by Barabanova [1] and energy type estimates. Show more

Keywords: Reaction‐diffusion systems, combustion, uniform estimates

Citation: Asymptotic Analysis, vol. 23, no. 3-4, pp. 195-216, 2000

Authors: Lezaun, Mikel

Article Type: Research Article

Abstract: In this paper, we deal with the dynamic of a model for the mass and heat transfer by a gaseous phase with an instantaneous chemical reaction, which is modeled by means of a subdifferential. To solve this problem, we use a penalization method and we prove that a maximal attractor describes the long‐time behaviour of the weak solutions. Furthermore, we prove the upper semicontinuity in L^{2} of the family of attractors related to the penalization approach of this problem.

Citation: Asymptotic Analysis, vol. 23, no. 3-4, pp. 217-238, 2000

Authors: Turowski, Gudrun

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 23, no. 3-4, pp. 239-256, 2000

Authors: Wright, Steve

Article Type: Research Article

Abstract: An incompressible fluid is assumed to satisfy the time‐dependent Stokes equations in a porous medium. The porous medium is modeled by a bounded domain in R^n that is perforated for each ε > 0 by ε‐dilations of a subset of R^n arising from a family of stochastic processes which generalize the homogeneous random fields. The solution of the Stokes equations on these perforated domains is homogenized as ε → 0 by means of stochastic two‐scale convergence in the mean, and the homogenized limit is shown to satisfy a two‐pressure Stokes system containing both deterministic and …stochastic derivatives and a Darcy‐type law with memory which generalizes the Darcy law obtained for fluid flow in periodically perforated porous media. Show more

Citation: Asymptotic Analysis, vol. 23, no. 3-4, pp. 257-272, 2000

Authors: Toader, Rodica

Article Type: Research Article

Abstract: We study the behaviour of solutions of relaxed wave equations with Dirichlet boundary conditions corresponding to a γ‐convergent sequence of measures. The model case is that of a sequence of domains with many small obstacles. Convergence results are proved for the solutions on finite time intervals.

Citation: Asymptotic Analysis, vol. 23, no. 3-4, pp. 273-290, 2000

Authors: Percivale, Danilo | Tomarelli, Franco

Article Type: Research Article

Abstract: The optimal asymptotic behaviour of the Korn–Poincaré inequality constant due to anysotropic shrinking of the open set is proved together with a description of an elastic‐perfectly plastic cantilever as a variational limit of an elastic micro‐fractured 2D‐body.

Citation: Asymptotic Analysis, vol. 23, no. 3-4, pp. 291-311, 2000

Authors: Neuss‐Radu, Maria

Article Type: Research Article

Abstract: Boundary layers are used in the homogenization of elliptic problems with periodically oscillating coefficients, for example when we want to improve the macroscopic approximation given by homogenization in the neighborhood of the boundary of a domain. For problems with a special geometry the boundary layers are defined on a semi‐infinite strip ]0,1[^{n-1}\times]0,\infty[\, , and their energies decrease exponentially with respect to the second variable. In our paper, we show that in general this decay property does not hold, i.e., we cannot get uniform exponential decay of the boundary layers.

Citation: Asymptotic Analysis, vol. 23, no. 3-4, pp. 313-328, 2000

Authors: Inoue, Atsushi | Nomura, Yuji

Article Type: Research Article

Abstract: In Random Matrix Theory (R.M.T.), Wigner’s semi‐circle law gives a well‐known corner‐stone. We report mathematical refinements of this law as an application of superanalysis. That is, using Efetov’s idea, we rewrite the average of the empirical measure of the eigenvalue distribution of the Hermitian Gaussian matrices (GUE) in a compact form. Careful calculations give not only the precise convergence rate of that law, but also the precise rate of the edge mobility.

Citation: Asymptotic Analysis, vol. 23, no. 3-4, pp. 329-375, 2000

Article Type: Other

Citation: Asymptotic Analysis, vol. 23, no. 3-4, pp. 377-377, 2000