Diffusion Limit of 1-D Small Mean Free Path of Radiative Transfer Equations in Bounded Domain

Abstract

In this paper, we consider the diffusion limit of the small mean free path for the radiative transfer equations, which describe the spatial transport of radiation in material. By using asymptotic expansions, we prove that the nonlinear transfer equation has a diffusion limit as the mean free path tends to zero, and moreover we study the boundary layer problem and mixed layer problem in bounded domain [0,1]. Then we show the validity of their asymptotic expansions relies only on the smoothness of boundary condition, and remove the Fredholm alternative and centering condition.