Acta mathematica scientia, Series B >
GLOBAL SOLUTIONS TO A HYPERBOLICPARABOLIC COUPLED SYSTEM WITH LARGE INITIAL DATA
Received date: 2008-11-27
Online published: 2009-05-20
Supported by
The research of Huijiang Zhao was supported by the National Natural Science Foundation of China (10871151). The research of Changjiang Zhu was supported by the National Natural Science Foundation of China (10625105 and 10431060), the Program for New Century Excellent Talents in University (NCET-04-0745)
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 L1-estimates and H2-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].
GUO Jun , XIAO Ji-Xiong , DIAO Hui-Jiang , SHU Chang-Jiang . GLOBAL SOLUTIONS TO A HYPERBOLICPARABOLIC COUPLED SYSTEM WITH LARGE INITIAL DATA[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 629 -641 . DOI: 10.1016/S0252-9602(09)60059-X
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