Global analysis of smooth solutions to a hyperbolic-parabolic coupled system

作     者：Yinghui ZHANG Haiying DENG Mingbao SUN 

作者机构：Department of Mathematics Hunan Institute of Science and Technology Yueyang 414006 China School of Mathematics and Statistics Central China Normal University Wuhan 430079 China Department of Mathematics Hunan First Normal College Changsha 410205 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2013年第8卷第6期

页      面：1437-1460页

核心收录：

学科分类：080901[工学-物理电子学] 07[理学] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 080401[工学-精密仪器及机械] 0804[工学-仪器科学与技术] 0803[工学-光学工程] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：国家自然科学基金 中国博士后科学基金 湖南省自然科学基金 

主　　题：Global analysis hyperbolic-parabolic system decay rate convex entropy 

摘      要：We investigate a model arising from biology, which is a hyperbolic- parabolic coupled system. First, we prove the global existence and asymptotic behavior of smooth solutions to the Cauchy problem without any smallness assumption on the initial data. Second, if the Hs ∩ Ll-norm of initial data is sufficiently small, we also establish decay rates of the global smooth solutions. In particular, the optimal L2 decay rate of the solution and the almost optimal L2 decay rate of the first-order derivatives of the solution are obtained. These results are obtained by constructing a new nonnegative convex entropy and combining spectral analysis with energy methods.