# American Institute of Mathematical Sciences

September  2003, 9(5): 1243-1262. doi: 10.3934/dcds.2003.9.1243

## Convergence to strong nonlinear rarefaction waves for global smooth solutions of $p-$system with relaxation

 1 Laboratory of Mathematical Physics, Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, P. O. Box 71010, Wuhan 430071, China, China

Received  July 2002 Revised  December 2002 Published  June 2003

This paper is concerned with the large time behavior of global smooth solutions to the Cauchy problem of the $p-$system with relaxation. Former results in this direction indicate that such a problem possesses a global smooth solution provided that the first derivative of the solutions with respect to the space variable $x$ are sufficiently small. Under the same small assumption on the global smooth solution, we show that it converges to the corresponding nonlinear rarefaction wave and in our analysis, we do not ask the rarefaction wave to be weak and the initial error can also be chosen arbitrarily large.
Citation: Huijiang Zhao, Yinchuan Zhao. Convergence to strong nonlinear rarefaction waves for global smooth solutions of $p-$system with relaxation. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1243-1262. doi: 10.3934/dcds.2003.9.1243
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