Boundary conditions and boundary layers for a multi-dimensional relaxation model

In this paper we study the linearized relaxation model of Katsoulakis and Tzavaras in a half-space with arbitrary space dimension n greater than or equal to 1. Our main interest is to establish the asymptotic equivalence of the relaxation system and its corresponding multi-dimensional equilibrium conservation law. We identify and rigorously justify a necessary and sufficient condition (which we refer to as stiff Kreiss condition, or SKC in short) on the boundary condition to guarantee the uniform stability of the initial-boundary value problem of the relaxation system independent of the relaxation rate. The asymptotic convergence and the corresponding boundary layer behavior are studied by Fourier-Laplace transform and a detailed asymptotic analysis. The SKC is shown to be more restrictive than the classical uniform Kreiss condition for all n greater than or equal to 1. (C) 2003 Elsevier Inc. All rights reserved.