非等熵Chaplygin气体测度值解存在性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (4): 833-841.

• 论文 • 下一篇

非等熵Chaplygin气体测度值解存在性

陈雨风¹(),陈停停^2,*(),王振¹()

¹ 武汉理工大学理学院武汉 430070
² 中国地质大学(武汉)数学物理学院武汉 430074

收稿日期:2020-01-02 出版日期:2020-08-26 发布日期:2020-08-20
通讯作者: 陈停停 E-mail:cyf20081015@163.com;chentt@cug.edu.cn;zwang@whut.edu.cn
作者简介:陈雨风, E-mail:cyf20081015@163.com|王振, E-mail:zwang@whut.edu.cn
基金资助:
国家自然科学基金(11771442);中国地质大学（武汉）中央高校基本科研业务费专项资金(CUGL180827)

The Existence of the Measure Solution for the Non-Isentropic Chaplygin Gas

Yufeng Chen¹(),Tingting Chen^2,*(),Zhen Wang¹()

¹ School of Science, Wuhan University of Technology, Wuhan 430070
² School of Mathematics and Physics, China University of Geoscience, Wuhan 430074

Received:2020-01-02 Online:2020-08-26 Published:2020-08-20
Contact: Tingting Chen E-mail:cyf20081015@163.com;chentt@cug.edu.cn;zwang@whut.edu.cn
Supported by:
the NSFC(11771442);the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan)(CUGL180827)

摘要/Abstract

摘要：

该文研究了一维非等熵Chaplygin气体动力学方程组的黎曼问题.考虑压力和内能均满足一般表示的情况下，利用特征分析的方法，分析经典弱解存在的充要条件.由于该弱解密度会出现集中的现象，因此会产生δ波.该文在Radon测度值解意义下，推导广义Rankine-Hugoniot条件，结合经典熵条件，构造一般黎曼问题的测度值解.该结果是等熵Chaplygin气体弱解存在性的推广.

关键词: 非等熵Chaplygin气体, 黎曼问题, 测度值解, 广义Rankine-Hugoniot条件

Abstract:

In this paper, we consider the Riemann problem of one-dimensional non-isentropic Chaplygin gas dynamics. In the case that the pressure and internal energy are general, we construct the classical solution by the characteristic analysis under a sufficient and necessary condition on the Riemann data. As the density ρ concentrates, the δ shock waves exist. According to the theory of Radon measure, the general Rankine-Hugoniot is induced. Combining with entropy condition, we obtain the measure solution for this problem. This extends the result for the isentropic Chaplygin gas.

Key words: Non-isentropic Chaplygin gas, Riemann problem, Measure solution, General Rankine-Hugoniot condition

中图分类号:

O175

陈雨风,陈停停,王振. 非等熵Chaplygin气体测度值解存在性[J]. 数学物理学报, 2020, 40(4): 833-841.

Yufeng Chen,Tingting Chen,Zhen Wang. The Existence of the Measure Solution for the Non-Isentropic Chaplygin Gas[J]. Acta mathematica scientia,Series A, 2020, 40(4): 833-841.

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非等熵Chaplygin气体测度值解存在性

The Existence of the Measure Solution for the Non-Isentropic Chaplygin Gas

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