Global existence and asymptotic behavior for a viscous, heat-conductive, one-dimensional real gas with fixed and constant temperature boundary conditions

Abstract

This paper is concerned with the global existence and asymptotic behaviour, as time tends to infinity, of solutions to the system for a nonlinear viscous, heat-conductive, one-dimensional real gas. Our results show that the global solution approaches to the solution in the $H^1$ norm to the corresponding stationary problem, as time tends to infinity.