Equilibrium-diffusion limit of the radiation model

We justify rigorously the equilibrium-diffusion limit of the model consists of a radiative transfer satisfied by the specific intensity of radiation coupled to a diffusion equation satisfied by the material temperature. For general initial data, we construct the existence of the solution to the coupled model in ${\mathbb{T}}^3$ by the Hilbert expansion and prove the convergence of the solutions to the limiting system in the equilibrium-diffusion regime. Moreover, the initial layer for the radiative density and the temperature are constructed to get the strong convergence in $L^{\mathrm{\infty }}$ norm. We also get the convergence rates about the intensity of radiation and temperature in this paper.