Diffusion Limit of a Small Mean Free Path of Radiative Transfer Equations with Absorbing Boundary Condition

Abstract

In this article, the nonlinear transfer equations with absorbing boundary condition, which describe the spatial transport of radiation in a material medium, are considered. We first establish the well-posedness of solutions for the radiative transfer equations based on the principle of contraction mapping and the comparison principle. Then we show that the radiative transfer equations have diffusion limits as the mean free path tends to zero if the specific intensity of radiation entering the system through the boundary of the domain is uniform with respect to the incoming direction. Our proof is based on asymptotic expansions. We show that the validity of these asymptotic expansions relies only on the smoothness of initial data and boundary functions, while two hypotheses, Fredholm alternative and centering condition, are removed.