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...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.展开更多
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.
文摘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.
