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.
"Global existence and asymptotic behavior for a viscous, heat-conductive, one-dimensional real gas with fixed and constant temperature boundary conditions." Adv. Differential Equations 7 (2) 129 - 154, 2002. https://doi.org/10.57262/ade/1356651848