Asymptotic stability of the stationary solution to an outflow problem for the compressible Navier-Stokes equations for a reacting mixture

Abstract

We investigate the large-time behavior of solutions to an outflow problem in one-dimensional half space for compressible Navier-Stokes equations for a reacting mixture. First, we show the existence and spatial decay rate of the stationary solution provided with the boundary data is small enough. Next, by means of the energy method and a Poincaré type inequality, we prove that the stationary solution is asymptotically stable under the small assumptions on the boundary data and the initial perturbation in the Sobolev space.