Asymptotic stability of viscous contact wave for the 1D radiation hydrodynamics system (Q550021)

This paper is concerned with the large time behavior of solutions to a radiating gas model, which is represented mathematically as a Cauchy problem for a one-dimensional hyperbolic-elliptic coupled system, with suitable given far field states. Suppose the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, then the authors construct a ``viscous contact wave'' for such a hyperbolic-elliptic system. Based on the energy methods and the ellipticity of the radiation flux equation, the authors prove that the ``viscous contact wave'' is asymptotically stable provided that the strength of contact discontinuity and the perturbation of the initial data are suitably small.