Nonstationary problem of complex heat transfer in a system of semitransparent bodies with radiation diffuse reflection and refraction boundary-value conditions

We consider a nonstationary initial-boundary value problem describing complex (radiative-conductive) heat transfer in a system of semitransparent bodies. To describe radiation propagation, we use the transport equation with radiation diffuse reflection and refraction boundary-value conditions. We take into account that the radiation intensity and optical properties of bodies depend on the radiation frequency. The unique solvability of a weak solution is established. The comparison theorem is proved. A priori estimates of a weak solution are obtained as well as its regularity.