# American Institute of Mathematical Sciences

May  2012, 17(3): 1075-1100. doi: 10.3934/dcdsb.2012.17.1075

## Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1D radiation hydrodynamics model

 1 Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

Received  August 2011 Revised  September 2011 Published  January 2012

In this paper we consider the large-time behavior of solutions for the Cauchy problem to a compressible radiating gas model, where the far field states are prescribed. This radiating gas model is represented by the one-dimensional system of gas dynamics coupled with an elliptic equation for radiation flux. When the corresponding Riemann problem for the compressible Euler system admits a solution consisting of a contact wave and two rarefaction waves, it is proved that for such a radiating gas model, the combination of viscous contact wave with rarefaction waves is asymptotically stable provided that the strength of combination wave is suitably small. This result is proved by a domain decomposition technique and elementary energy methods.
Citation: Feng Xie. Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1D radiation hydrodynamics model. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 1075-1100. doi: 10.3934/dcdsb.2012.17.1075
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