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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (6): 665-674.doi: https://doi.org/10.1007/s10483-010-1301-9

• Articles •    下一篇

The Riemann problem for nonlinear degenerate wave equations

孙文华1 盛万成2   

  1. 1. School of Mathematics and Information Sciences, Shandong University of Technology,Zibo 255049, Shandong Province, P. R. China;
    2. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
  • 收稿日期:2009-12-21 修回日期:2010-05-10 出版日期:2010-06-01 发布日期:2010-06-01

The Riemann problem for nonlinear degenerate wave equations

SUN Wen-Hua1, SHENG Wan-Cheng2   

  1. 1. School of Mathematics and Information Sciences, Shandong University of Technology,Zibo 255049, Shandong Province, P. R. China;
    2. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
  • Received:2009-12-21 Revised:2010-05-10 Online:2010-06-01 Published:2010-06-01

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1303

被引次数

10

摘要： This paper studies the Riemann problem for a system of nonlinear degenerate wave equations in elasticity. Since the stress function is neither convex nor concave, the shock condition is degenerate. By introducing a degenerate shock under the generalized shock condition, the global solutions are constructively obtained case by case.

关键词: degenerate wave equations, Riemann problem, rarefaction wave, shock wave, degenerate shock

Abstract: This paper studies the Riemann problem for a system of nonlinear degenerate wave equations in elasticity. Since the stress function is neither convex nor concave, the shock condition is degenerate. By introducing a degenerate shock under the generalized shock condition, the global solutions are constructively obtained case by case.

Key words: degenerate wave equations, Riemann problem, rarefaction wave, shock wave, degenerate shock

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