Initial-boundary value problem for a radiative transfer equation with generalized matching conditions

We consider the Cauchy problem for a non-stationary radiative transfer equation in a three-dimensional multicomponent medium with generalized matching conditions. These matching condition describe Fresnel and diffuse reflection and refraction at the interfaces. The existence and uniqueness of a solution of the initial-boundary value problem is proved. We construct a Monte-Carlo numerical method designed to find a solution that accounts for the space-time localization of radiation sources. Computational experiments were carried out and their results presented.