Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1Dradiation hydrodynamics model

Feng Xie

doi:10.3934/dcdsb.2012.17.1075

Article Contents

2012, Volume 17, Issue 3: 1075-1100. Doi: 10.3934/dcdsb.2012.17.1075

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

Feng Xie^1,

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

Received: August 2011

Revised: September 2011

Published: May 2012

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Abstract

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.

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Mathematics Subject Classification: 35L65, 35B40, 35Q35.

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