数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (3): 629-641.doi: 10.1016/S0252-9602(09)60059-X

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GLOBAL SOLUTIONS TO A HYPERBOLICPARABOLIC COUPLED SYSTEM WITH LARGE INITIAL DATA

郭军,肖继雄,赵会江,朱长江   

  1. 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
  • 收稿日期:2008-11-27 出版日期:2009-05-20 发布日期:2009-05-20
  • 基金资助:

    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)

GLOBAL SOLUTIONS TO A HYPERBOLICPARABOLIC COUPLED SYSTEM WITH LARGE INITIAL DATA

 GUO Jun, XIAO Ji-Xiong, DIAO Hui-Jiang, SHU Chang-Jiang   

  1. 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
  • Received:2008-11-27 Online:2009-05-20 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)

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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 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].

关键词: hyperbolic-parabolic coupled system, local solution, global solution, entropy-entropy flux, energy estimates

Abstract:

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].

Key words: hyperbolic-parabolic coupled system, local solution, global solution, entropy-entropy flux, energy estimates

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