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

In this paper we consider the large-timebehavior 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 asolution consisting of a contact wave and two rarefactionwaves, it is proved that for such a radiating gas model, the combination of viscous contact wave with rarefaction waves isasymptotically stable provided that the strength of combination wave issuitably small. This result is proved by a domain decomposition technique and elementary energy methods.