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Zeitschrift für Analysis und ihre Anwendungen


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Volume 23, Issue 3, 2004, pp. 607–630
DOI: 10.4171/ZAA/1213

Published online: 2004-09-30

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

SHU-YI ZHANG[1] and Ya-Guang Wang[2]

(1) Jiao Tong University, Shanghai, China
(2) Jiao Tong University, Shanghai, China

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.

Keywords: Relaxation system, initial-boundary value problems, boundary layers

ZHANG SHU-YI, Wang Ya-Guang: Well-Posedness and Asymptotics for Initial Boundary Value Problems of Linear Relaxation Systems in One Space Variable. Z. Anal. Anwend. 23 (2004), 607-630. doi: 10.4171/ZAA/1213