Initial-Boundary Value Problems for One-Dimensional pth Power Viscous Reactive Gas with Density-Dependent Viscosity

Although there are many results on the global solvability and the precise description of the large time behaviors of solutions to the initial-boundary value/Cauchy problem of the one-dimensional pth power viscous reactive gas with positive constant viscosity, no result is available up to now for the corresponding problems with density-dependent viscosity. The main purpose of this paper is to study the global existence and asymptotic behavior of solutions to three types of initial-boundary value problems of 1d pth power viscous reactive gas with density-dependent viscosity and large initial data. The key ingredient in our analysis is to deduce the positive lower and upper bounds on both the specific volume and the absolute temperature.