Stationary wave associated with an inflow problem in the half-line for viscous heat-conductive gas (Q2891094)

The authors study the large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. They consider an inflow problem where the gas enters into the region through the boundary, and the corresponding stationary solution is shown to be time-asymptotically stable in both the subsonic and transonic cases. The proof of the asymptotic stability is based on a priori estimates of the perturbation from the stationary solution, which are derived by a standard energy method, provided the boundary perturbation and the initial perturbation are sufficiently small in a certain Sobolev norm.