Unique solvability of a stationary radiative–conductive heat transfer problem in a semitransparent body with absolutely black inclusions

Abstract

We consider a stationary boundary value problem describing a radiative–conductive heat transfer in a semitransparent body with absolutely black 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. Besides, we proved the comparison theorems and established the results on improving the properties of solutions with increasing exponents of data summability.