Abstract:

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.

Key words: Hyperbolic-elliptic coupled system, rarefaction wave, asymptotic stability, L²-energy method