Hilbert expansion of a coupled model for radiative transfer in a unit disk: General initial and boundary data

We consider the diffusion asymptotic of a coupled model arising in radiative transfer in a unit disk with general initial and boundary data. The model consists of a kinetic equation satisfied by the specific intensity of radiation coupled a nonhomogeneous heat equation satisfied by the material temperature. For the general initial and boundary data, we construct the solution by Hilbert Expansion and prove the non-equilibrium diffusion limit of solutions to the initial-boundary value problem for the coupled model. Furthermore, the strong initial and boundary layers of the intensity will arise. Note that we also get the convergence rates about the intensity of radiation and temperature in this paper.