ASYMPTOTIC DECAY TOWARD RAREFACTION WAVE FOR A HYPERBOLIC-ELLIPTIC COUPLED SYSTEM ON HALF SPACE

作     者：Ruan Lizhi Zhu Changjiang 

作者机构：Laboratory of Nonlinear Analysis Department of Mathematics Central China Normal University Wuhan 430079 Department of Applied Mathematics S. C. Univ. Nationalities Wuhan 430074 China Laboratory of Nonlinear Analysis Department of Mathematics Central China Normal University Wuhan 430079 China 

出 版 物：《Journal of Partial Differential Equations》 (偏微分方程（英文版）)

年 卷 期：2008年第21卷第2期

页      面：173-192页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The research was supported by the National Natural Science Foundation of China #10625105 and #10431060  the Program for New Century Excellent Talents in University #NCET-04-0745. Acknowledgement Authors would like to thank the anonymous referee for his/her helpful suggestions and comments 

主　　题：Hyperbolic-elliptic coupled system rarefaction wave asymptoticdecay rate half space L2-energy method L1-estimate. 

摘      要：We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R＋ = （0, ∞）,with the Dirichlet boundary condition u（0, t） = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58（2004）, 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u＋. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution （u, q） is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem.