About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 691429, 7 pages
http://dx.doi.org/10.1155/2014/691429
Research Article

Global Existence of Solutions for a Nonstrictly Hyperbolic System

1Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China
2College of Health Administration, Anhui Medical University, Hefei 230032, China
3Laboratoire Ondes and Milieux Complexes UMR 6294, CNRS-Universite du Havre, 76058 Le Havre, France

Received 16 November 2013; Accepted 14 February 2014; Published 31 March 2014

Academic Editor: Adem Kilicman

Copyright © 2014 De-yin Zheng et al. 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

We obtain the global existence of weak solutions for the Cauchy problem of the nonhomogeneous, resonant system. First, by using the technique given in Tsuge (2006), we obtain the uniformly bounded estimates and when is increasing (similarly, and when is decreasing) for the -viscosity and -flux approximation solutions of nonhomogeneous, resonant system without the restriction or as given in Klingenberg and Lu (1997), where and are Riemann invariants of nonhomogeneous, resonant system; is a uniformly bounded function of depending only on the function given in nonhomogeneous, resonant system, and is the bound of . Second, we use the compensated compactness theory, Murat (1978) and Tartar (1979), to prove the convergence of the approximation solutions.