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Advances in Mathematical Physics
Volume 2017, Article ID 3276182, 12 pages
https://doi.org/10.1155/2017/3276182
Research Article

The Perturbed Riemann Problem for Special Keyfitz-Kranzer System with Three Piecewise Constant States

School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong Province 264025, China

Correspondence should be addressed to Chun Shen; moc.anis@1463nuhcnehs

Received 1 June 2017; Accepted 27 July 2017; Published 29 August 2017

Academic Editor: Pavel Kurasov

Copyright © 2017 Yuhao Jiang and Chun Shen. 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

The Riemann problem for a special Keyfitz-Kranzer system is investigated and then seven different Riemann solutions are constructed. When the initial data are chosen as three piecewise constant states under suitable assumptions, the global solutions to the perturbed Riemann problem are constructed explicitly by studying all occurring wave interactions in detail. Furthermore, the stabilities of solutions are obtained under the specific small perturbations of Riemann initial data.