GLOBAL SOLUTIONS TO A HYPERBOLIC-PARABOLIC COUPLED SYSTEM WITH LARGE INITIAL DATA  

作　　者：郭军 肖继雄 赵会江 朱长江 

机构地区：[1]School of Mathematics and Statistics, Wuhan University,Wuhan 430072, China [2]Laboratory of Nonlinear Analysis, School of Mathematics and Statistics,Central China Normal University,Wuhan 430079, China

出　　处：《Acta Mathematica Scientia》2009年第3期629-641,共13页数学物理学报（B辑英文版）

基　　金：Huijiang Zhao was supported by the National Natural Science Foundation of China (10871151);Changjiang Zhu was supported by the National Natural Science Foundation of China (10625105 and 10431060);the Program for New Century Excellent Talentsin University (NCET-04-0745)

摘　　要：This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].

关 键 词：hyperbolic-parabolic coupled system local solution global solution entropy-entropy flux energy estimates 

分 类 号：O175[理学—数学]