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

• Published in: Acta mathematica scientia Vol. 29; no. 3; pp. 629 - 641
• Main Author: 郭军 肖继雄 赵会江 朱长江
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2009
• Subjects: 35K65; 35L80; 35M10; Cauchy问题; energy estimates; entropy-entropy flux; global solution; hyperbolic-parabolic coupled system; local solution; 地方标准; 熵通量; 耦合系统; 能量估计; 起算数据; 迭代技术; energy estimates; hyperbolic-parabolic coupled system; 35L80; entropy-entropy flux; local solution; 35M10; global solution; 35K65
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(09)60059-X

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].