Two-dimensional Riemann problem involving three contact discontinuities for 2 x 2 hyperbolic conservation laws in anisotropic media

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:428

Article

Pang, Yicheng^1,2  Yang, Hanchun² 

[1] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China

[2] Yunnan Univ, Dept Math, Kunming 650091, Peoples R China

关键词: Contact discontinuity;    Envelope rarefaction wave;    Systems of conservation laws;    Two-dimensional Riemann problem;   

DOI  :  10.1016/j.jmaa.2015.02.042

来源: Elsevier

【 摘 要 】

In this study, we consider the two-dimensional Riemann problem for a system of conservation laws, which models polymer flooding in an anisotropic oil reservoir. The initial data are constants in three sectors centered at the origin, which only involve three contact discontinuities. By the generalized characteristic analysis method and the phase plane analysis method, we find that the solutions are not unique for certain values of the initial data. We propose an additional stability condition for the interaction of the contact discontinuities. By this stability condition, all of the exact solutions and their corresponding criteria can be obtained. The solutions exhibit various geometrical structures. In particular, envelope rarefaction waves develop in some solutions. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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