Abstract
This paper concerns 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 rates of solutions are also derived provided the initial data satisfy an additional L1 condition. Meanwhile, the same decay rates of the solutions to the approximation system without thermal conductivity could also be established.
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