零压相对论欧拉方程组含有狄拉克函数初值的黎曼问题

数学物理学报 ›› 2014, Vol. 34 ›› Issue (5): 1083-1092.

零压相对论欧拉方程组含有狄拉克函数初值的黎曼问题

李建业|邵志强**

福州大学数学与计算机科学学院福州350108

收稿日期:2013-01-17 修回日期:2014-03-25 出版日期:2014-10-25 发布日期:2014-10-25
基金资助:
福建省自然科学基金(2012J01006)资助.

The Riemann Problem with Delta Initial Data for the Zero-Pressure Relativistic Euler Equations Hyperbolic Systems of Conservation Laws

LI Jian-Ye, SHAO Zhi-Qiang**

College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108

Received:2013-01-17 Revised:2014-03-25 Online:2014-10-25 Published:2014-10-25
Supported by:
福建省自然科学基金(2012J01006)资助.

摘要/Abstract

摘要：

研究一维零压相对论欧拉双曲守恒律系统含有狄拉克函数的初值条件的黎曼问题. 借助特征线分析方法, 求出了四种不同情形下的整体广义解, 包括了含有狄拉克激波.

关键词: 相对论欧拉方程组, 广义Rankine-Hugoniot条件, Delta -激波, 线性退化, 熵条件中

Abstract:

In this paper, we solve the Riemann problem with the initial data containing Dirac delta functions for the zero-pressure relativistic Euler hyperbolic systems of conservation laws. With characteristic analysis, under suitably generalized Rankine-Hugoniot relation and entropy condition, we constructively obtain the global generalized solutions that explicitly exhibit four kinds of different structure involving delta shock waves.

Key words: Relativistic Euler equations, Generalized Rankine-Hugoniot relation, Delta shock wave, Linearly degenerate, Entropy condition

中图分类号:

35L65

李建业, 邵志强. 零压相对论欧拉方程组含有狄拉克函数初值的黎曼问题[J]. 数学物理学报, 2014, 34(5): 1083-1092.

LI Jian-Ye, SHAO Zhi-Qiang. The Riemann Problem with Delta Initial Data for the Zero-Pressure Relativistic Euler Equations Hyperbolic Systems of Conservation Laws[J]. Acta mathematica scientia,Series A, 2014, 34(5): 1083-1092.

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