带群集耗散项的零压流方程的扰动黎曼问题

数学物理学报 ›› 2020, Vol. 40 ›› Issue (1): 49-62.

带群集耗散项的零压流方程的扰动黎曼问题

张庆玲,巴英

^{江汉大学数学与计算机科学学院数学系武汉 430056}

收稿日期:2018-05-15 出版日期:2020-01-26 发布日期:2020-04-08
作者简介:张庆玲
基金资助:
武汉市教育局教学研究重点项目(2017007)

The Perturbed Riemann Problem for the Pressureless Euler Equations with a Flocking Dissipation

Qingling Zhang,Ying Ba

^{Department of Mathematics, School of Mathematics and Computer Sciences, Jianghan University, Wuhan 430056}

Received:2018-05-15 Online:2020-01-26 Published:2020-04-08
Supported by:
武汉市教育局教学研究重点项目(2017007)

摘要/Abstract

摘要：

该文通过分析带群集耗散项的零压流方程初始波含狄拉克激波的波的相互作用，研究了其初值含三片常值和初值含狄拉克测度的两种扰动黎曼问题.当初值为三片常值时，通过广义Rankine-Hugoniot条件和广义熵条件，该文构造性地得到了整体解.进一步地，利用弱解的稳定性理论，通过分析初值为三片常值情形下解的结构并取极限，该文得到了初值含狄拉克测度的扰动黎曼问题的整体解.另外，在构造解的过程中，还引入了一种新的非经典解：狄拉克接触间断解.

关键词: 零压流, 黎曼问题, 狄拉克激波, 真空, 群集耗散, 波的相互作用

Abstract:

In this paper, the wave interactions involving the delta shock waves for the pressureless Euler equations with a flocking dissipation is considered and two kinds of perturbed Riemann problems are studied. The global existence of the generalzied solutions is obtained constructively by using the generalized Rankine-Hugoniot conditions and the entropy condition when the initial data are three piecewise constant states. By analyzing the global structure and the limit under the stability theory of weak solutions, the global soution for the delta inital data problem are constructively obtained. Moreover, a new kind of nonclassical wave -delta contact discontinuity has appeared in it.

Key words: Pressureless Euler equations, Riemann problem, Delta shock wave, Vacuum state, Flocking dissipation, Interaction

中图分类号:

O175.27

张庆玲,巴英. 带群集耗散项的零压流方程的扰动黎曼问题[J]. 数学物理学报, 2020, 40(1): 49-62.

Qingling Zhang,Ying Ba. The Perturbed Riemann Problem for the Pressureless Euler Equations with a Flocking Dissipation[J]. Acta mathematica scientia,Series A, 2020, 40(1): 49-62.

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