带群集耗散项的零压流方程的扰动黎曼问题

Abstract

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

CLC Number:

O175.27

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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References 27

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

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