数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 825-841.doi: 10.1016/S0252-9602(12)60064-2

• 论文 •    下一篇

THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE ONE-DIMENSIONAL CHAPLYGIN GAS EQUATIONS

王振1, 张庆玲1,2   

  1. 1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
    2. School of Mathematics and Computer Sciences, Jianghan University, Wuhan 430056, China
  • 收稿日期:2010-11-09 修回日期:2011-04-27 出版日期:2012-05-20 发布日期:2012-05-20
  • 基金资助:

    This work is partially supported by National Natural Science Foundation of China (10871199).

THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE ONE-DIMENSIONAL CHAPLYGIN GAS EQUATIONS

 WANG Zhen1, ZHANG Qing-Ling1,2   

  1. 1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
    2. School of Mathematics and Computer Sciences, Jianghan University, Wuhan 430056, China
  • Received:2010-11-09 Revised:2011-04-27 Online:2012-05-20 Published:2012-05-20
  • Supported by:

    This work is partially supported by National Natural Science Foundation of China (10871199).

摘要:

In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.

关键词: Chaplygin gas equations, Riemann problem, delta-shocks, generalized Rankine-Hugoniot conditions, generalized solutions

Abstract:

In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.

Key words: Chaplygin gas equations, Riemann problem, delta-shocks, generalized Rankine-Hugoniot conditions, generalized solutions

中图分类号: 

  • 35L65