ASYMPTOTIC STABILITY OF SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR SCALAR VISCOUS CONSERVATION LAWS CORRESPONDING TO RAREFACTION WAVES

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：暨南大学数学系 广东 广州 510632 广西大学数学和信息科学系 广西 南宁 530004 

出 版 物：《Systems Science and Mathematical Sciences》 (SYSTEMS SCIENCE AND MATHEMATICAL SCIENCES)

年 卷 期：1999年第12卷第4期

页      面：366-377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：国务院侨办基金 广西教育厅项目 广西自然科学基金 

主　　题：Viscous conservation law rarefaction wave asymptotic stability boundary. 

摘      要：This paper is concerned with the asymptotic behaviors of solutions of thegeneral initial-boundary value problem to scalar viscous conservation law uxx on R+ with the conditions u（0, t） = u-（t） u-（t ）,u（x,0） = u0（x） u+（x-）, where f（u） 0 for all u under consideration, u- 0 admits the rarefaction wave. Ourproblem is divided into five cases depending on the signs of the characteristic speeds of the boundary state u- at t= and the far field state u+ = u（+）. Both the globalexistence of the solution and the asymptotic stability are shown in all cases.