Joint with Professor Zhouping Xin.

We study the asymptotic equivalence of a general linear system of one-dimensional conservation laws and the corresponding relaxation model proposed by Jin and Xin [Comm. Pure Applied Math., 48 (1995), no. 3, 235-276] 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 refer to Stiff Kreiss Condition) 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 Stiff Kreiss Condition 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 Laplace transform and a matched asymptotic analysis.

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