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The present paper is concerned with large-time behavior of solutions to anoutflow problem for an ideal polytropic model of compressible viscous gases inone-dimensional half space, and with a convergence rate of solutions toward acorresponding stationary solution. With the aid of center manifold theory, weprove the existence of the stationary solution, under a smallness condition onthe boundary data. We also investigate, by employing an energy method, the timeasymptotic stability of the stationary solution under suitable smallnessassumptions, and estimate the convergence rate which coincides with the spatialdecay rate of the initial perturbation. The proof is mainly based on a prioriestimates, which are derived by a time and space weighted energy method.

Stationary waves to viscous heat-conductive gases in half space: existence, stability and convergence rate