Stiff well-posedness and asymptotic convergence for a class of linear relaxation systems in a quarter plane

摘要

In this paper we study the asymptotic equivalence of a general linear system of 1-dimensional conservation laws and the corresponding relaxation model proposed by S. Jin and Z. Xin (1995, Comm. Pure Appl. Math. 48, 235-277) in the limit of small relaxation rate. The main interest is this asymptotic equivalence in the presence of physical boundaries. We identify and rigorously justify a necessary and sufficient condition (which we call the Stiff Kreiss Condition, or SKC in short) on the boundary condition to guarantee the uniform well-posedness of the initial boundary value problem for the relaxation system independent of the rate of relaxation. The SKC is derived and simplified by using a normal mode analysis and a conformal mapping theorem. The asymptotic convergence and boundary layer behavior are studied by the Laplace transform and a matched asymptotic analysis. An optimal rate of convergence is obtained. (C) 2000 Academic Press. [References: 17]