Global existence and large-time behavior of solutions to the Cauchy problem of one-dimensional viscous radiative and reactive gas

Abstract

In this paper we consider the global existence and large-time behavior of solutions of one-dimensional viscous radiative and reactive gas with large initial data. In precedent studies the case for the initial-boundary value problem in bounded domain has been investigated and our main purpose focuses on the corresponding problem in unbounded domain. If the initial data is a large perturbation of a non-vacuum constant equilibrium state and is assumed to be without vacuum, mass concentrations, or vanishing temperatures, then we can show that its Cauchy problem admits a unique global smooth non-vacuum solution which tends time-asymptotically to such an equilibrium state. The key point in the analysis is to deduce the uniform positive lower and upper bounds on the specific volume and the absolute temperature.