  This paper concerns with the large time behavior of solutions to a diffusion
approximation radiation hydrodynamics model when the initial data is a small
perturbation around an equilibrium state. The global-in-time well-posedness of
solutions is achieved in Sobolev spaces depending on the Littlewood-Paley
decomposition technique together with certain elaborate energy estimates in
frequency space. Moreover, the optimal decay rate of the solution is also
yielded provided the initial data also satisfy an additional $L^1$ condition.
Meanwhile, the similar results of the diffusion approximation system without
the thermal conductivity could be also established.
