Nonstationary radiative-conductive heat transfer problem in an absolutely black body with semitransparent inclusions

We consider a nonstationary initial-boundary value problem governing a radiative-conductive heat transfer in an absolutely black body with semitransparent inclusions. To describe the radiative transfer, the integro-differential radiative transfer equation is used. We do not take into account the dependence of the radiation intensity and the properties of semitransparent materials on the radiation frequency. We proved at the first time the unique solvability of this problem. In addition, we proved the stability of solutions with respect to data, established a comparison theorem and results on improving the properties of solutions with an increasing on the summability of the data.