Nonlinear stability of a composite wave pattern for a viscous, heat-conducting, radiative, and reactive gas with large initial perturbation

In this paper, we investigate the nonlinear stability of a composite wave pattern consisting of viscous contact wave and rarefaction waves to the Cauchy problem of a one-dimensional viscous, heat-conducting, radiative, and reactive gas under large initial perturbation and for the case when the viscosity is a positive constant. Compared with the case for ideal polytropic gases, it is not so obvious to see whether the pressure is a convex function of the specific volume and the entropy or not for the case considered in this paper, while such a convex property plays an essential role in the analysis. We find that the smallness of the radiation constant is a sufficient condition to guarantee the convexity of the pressure. The key point in the analysis is to deduce the uniform positive lower and upper bounds on the specific volume and the absolute temperature, which are independent of the radiation constant.