Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (6): 2313-2322.doi: 10.1016/S0252-9602(11)60403-7

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THE RIEMANN PROBLEM FOR THE NONLINEAR DEGENERATE WAVE EQUATIONS

 Liu Xiaomin1,2, Wang Zhen1   

  1. 1. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China;
    2. Graduate School of the Chinese Academy of Sciences, Beijing 100039, China
  • Received:2011-10-18 Online:2011-11-20 Published:2011-11-20
  • Supported by:

    Supported by the National Natural Science Foundation of China (11171340).

Abstract:

In this paper we consider the Riemann problem for the nonlinear degenerate wave equations. This problem has been studied by Sun and Sheng, however the so-called degenerate shock solutions did not satisfy the R-H condition. In the present paper, the Riemann solutions of twelve regions in the v -u plane are completely constructed by the Liu-entropy condition. Our Riemann solutions are very different to that one obtained by Sun and Sheng in some regions.

Key words: degenerate wave equations, Riemann problems, not strictly hyperbolic, Liu-entropy condition

CLC Number: 

  • 35L65
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