ASYMPTOTIC STABILITY OF VISCOUS SHOCK PROFILE FOR NON-CONVEX SYSTEM OF ONE-DIMENSIONAL VISCOELASTIC MATERIALS WITH BOUNDARY EFFECT

作     者：LIU Hongxia (Department of Mathematics, Jinan University, Guangzhou 510632, China) PAN Tao (Department of Mathematics and Information Science, Guangxi University, Nanning 530004, China) LIU Hongxia (Department of Mathematics, Jinan University, Guangzhou 510632, China) PAN Tao (Department of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

作者机构：暨南大学 广东 广州 510632 广西大学 广西 南宁 530004 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2001年第14卷第4期

页      面：425-437页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：To complete this work the first author is supported in part by the National Natural Science Foundationof China (19901012) 

主　　题：Viscous shock profile asymptotic stability non-convex system boundary. 

摘      要：This paper is concerned with the asymptotic behavior of solution to the initial-boundary value problem on the half space R+ for a one-dimensional non-convex system of viscoelastic materials. The initial data has constant state at infinity and the velocity is imposed zero at the boundary x = 0. By virture of the boundary effect, the solution is expected to behave as outgoing viscous shock profile. When the initial data is suitably close to the corresponding outgoing viscous shock profile which is suitably away from the boundary, it is proved that the unique global solution exists in time and tends toward the properly shifted shock profile as the time goes to infinity. The result is given by a weighted energy method.