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.
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SHU-YI ZHANG, Ya-Guang Wang, Well-Posedness and Asymptotics for Initial Boundary Value Problems of Linear Relaxation Systems in One Space Variable. Z. Anal. Anwend. 23 (2004), no. 3, pp. 607–630DOI 10.4171/ZAA/1213