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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 187217, 14 pages
http://dx.doi.org/10.1155/2013/187217
Research Article

On a Nonsymmetric Keyfitz-Kranzer System of Conservation Laws with Generalized and Modified Chaplygin Gas Pressure Law

Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

Received 2 June 2013; Revised 20 October 2013; Accepted 25 October 2013

Academic Editor: Stephen C. Anco

Copyright © 2013 Hongjun Cheng and Hanchun Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is devoted to the study of a nonsymmetric Keyfitz-Kranzer system of conservation laws with the generalized and modified Chaplygin gas pressure law, which may admit delta shock waves, a topic of interest. Firstly, we solve the Riemann problems with piecewise constant data having a single discontinuity. For the generalized Chaplygin gas pressure law, the solution consists of three different structures: , , and . Existence and uniqueness of delta shock solution are established under the generalized Rankine-Hugoniot relation and entropy condition. For the modified Chaplygin gas pressure law, the structures of solution are and . Secondly, we discuss the limits of Riemann solutions for the modified Chaplygin gas pressure law as the pressure law tends to the generalized Chaplygin gas one. In particular, for some cases, the solution tends to a delta shock wave, and it is different from the delta shock wave for the generalized Chaplygin gas pressure law with the same initial data. Thirdly, we simulate the Riemann solutions and examine the formation process of delta shock wave by employing the Nessyahu-Tadmor scheme. The numerical results are coincident with the theoretical analysis.