Asymptotic stability of rarefaction wave for hyperbolic-elliptic coupled system in radiating gas*

In this article, authors study the Cauch problem for a model of hyperbolic-elliptic coupled system derived from the one–dimensional system of the radiating gas. By considering the initial data as a small disturbances of rarefaction wave of inviscid Burgers equation, the global existence of the solution to the corresponding Cauchy problem and asymptotic stability of rarefaction wave is proved. The analysis is based on a priori estimates and L2-energy method.