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

doi:10.1016/S0252-9602(12)60064-2

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

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

王振¹, 张庆玲^1,2

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-Ling^1,2

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/Abstract

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:

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

中图分类号:

35L65

王振, 张庆玲. THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE ONE-DIMENSIONAL CHAPLYGIN GAS EQUATIONS[J]. 数学物理学报(英文版), 2012, 32(3): 825-841.

WANG Zhen, ZHANG Qing-Ling. THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE ONE-DIMENSIONAL CHAPLYGIN GAS EQUATIONS[J]. Acta mathematica scientia,Series B, 2012, 32(3): 825-841.

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

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

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