Theoretical and numerical analysis of an initial-boundary value problem for the radiative transfer equation with Fresnel matching conditions

A Cauchy problem for the time-dependent radiative transfer equation in a three-dimensional multicomponent medium with generalized matching conditions describing Fresnel reflection and refraction at the interface of the media is considered. The unique solvability of the problem is proven, a Monte Carlo method for solving the initial-boundary value problem is developed, and computational experiments for different implementations of the algorithm are conducted.