The outflow problem for the radiative and reactive gas: existence, stability and convergence rate

Abstract

Abstract In this paper, we show that the small-amplitude stationary solutions are time-asymptotically stable to the half-space problem for the one-dimensional radiative and reactive gas (pressure p = R ρ θ + a 3 θ 4 , internal energy e = C v θ + a ρ θ 4 ) provided that the initial perturbation is sufficiently small in some weighted Sobolev spaces. We also obtain the convergence rate of global solutions toward corresponding stationary solutions. The proofs are given by a weighted energy method. A key point is to capture the positivity of the energy dissipation functional and boundary terms with suitable space weight functions and using the precise estimates about stationary solutions.