Diffusion Limit of Small Mean Free Path of Transfer Equation in

Abstract

This article is devoted to establish the well-posedness of solutions and diffusion limit of the small mean free path of the nonlinear transfer equations, which describes the spatial transport of radiation in a material medium. By using the comparison principle, we obtain the lower bound and upper bound of the solution, and then we prove the existence and uniqueness of the global solution. We show that the nonlinear transfer equation has a diffusion limit as the mean free path tends to zero. Our proof is based on asymptotic expansions. We show that the validity of these asymptotic expansions relies only on the smoothness of initial data, while two hypotheses, Fredholm alternative and centering condition, are removed.