Diffusion asymptotics of a coupled model for radiative transfer without thermal diffusion effects: Ill-prepared initial data

This article studies the asymptotic analysis of a coupled model arising in radiative transfer in T 3 with one-speed velocity without thermal diffusion effects. The model consists of a kinetic equation satisfied by the specific intensity of radiation coupled to a transport equation satisfied by the material temperature. We combine the moment method with Hilbert expansion to show the radiative intensity can be approximated by the sum of interior solution and initial layer. We also show the solution satisfied by the temperature can be approximated by the interior solution.