Radiative Transfer in Two Adjoining Media: The Continuity of Thermal Flux and the Existence and Uniqueness of Solutions

The spatial transport of radiation in two adjoining media and the continuity of flux at the interface are considered. As usual, we assume that the material is in local thermodynamic equilibrium. First in the absence of hydrodynamic motion and thermal diffusion, the existence and uniqueness of a global solution of the classical radiative transfer equations with the absorbing boundary condition is derived. But the continuity of thermal flux at the interface of two materials cannot be preserved in this classical model. To preserved the continuity of thermal flux at the interface, we consider radiative transfer equations modified by thermal diffusion. The existence and uniqueness of a global solution of this modified radiative transfer equation is also derived.