Unique solvability of a nonstationary problem of radiative-conductive heat exchange in a system of semitransparent bodies

摘要

A nonstationary initial boundary value problem describing the radiative-conductive heat exchange in a system of semitransparent bodies is considered. The radiation transfer equation with boundary conditions of mirror reflection and refraction according to the Fresnel laws is used to describe the propagation of radiation. The dependence of the radiation intensity and the optical properties of bodies on the radiation frequency is taken into account. The existence and uniqueness of a weak solution are proved. A comparison theorem is proved. Some a priori estimates for the weak solution are derived and its regularity is proved.