Well-Posedness and Asymptotics for Initial Boundary Value Problems of Linear Relaxation Systems in One Space Variable

Abstract

We study the well-posedness and relaxation limit for the initial boundary value problem of a general linear hyperbolic system with a relaxation term in one space variable. We mainly consider the asymptotic convergence and the boundary layer behavior under the sub-characteristic condition and the stiff Kreiss condition when the relaxation rate goes to zero, which generalizes recent results of Xin and Xu [J. Diff. Eqs. 167 (2000) 388–437] for homogeneous problems to the non-homogeneous case.