Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 782306, 30 pages
http://dx.doi.org/10.5402/2012/782306
Research Article

The Inviscid Limits to Piecewise Smooth Solutions for a General Parabolic System

School of Mathematical Sciences, South China Normal University, Guang Zhou 510631, China

Received 13 October 2011; Accepted 26 October 2011

Academic Editors: U. Kulshreshtha and M. Znojil

Copyright Β© 2012 Shixiang Ma. 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 study the viscous limit problem for a general system of conservation laws. We prove that if the solution of the underlying inviscid problem is piecewise smooth with finitely many noninteracting shocks satisfying the entropy condition, then there exist solutions to the corresponding viscous system which converge to the inviscid solutions away from shock discontinuities at a rate of πœ€1 as the viscosity coefficient πœ€ vanishes.