The existence and stability of stationary solutions of the inflow problem for full compressible Navier-Stokes-Poisson system

In this paper, we consider an inflow problem for the non-isentropic Navier-Stokes-Poisson system in a half line (0, infinity). For the general gas including ideal polytropic gas, we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4 x 4 system of autonomous ordinary differential equations. We also show the time asymptotic stability of the stationary solutions with small strength under smallness assumptions on the initial perturbations by using an elementary energy method.