Unique Solvability of Stationary Radiative-Conductive Heat Transfer Problem in a System of Semitransparent Bodies

Abstract

We consider the boundary value problem for a system of differential equations consisting of the stationary nonlinear heat equation and the integro-differential radiative transfer equation and describing stationary radiative-conductive heat transfer in a system of semitransparent bodies, taking into account the effects of reflection and refraction of radiation according to the Fresnel laws at the boundaries of bodies. We take into account the dependence of radiation intensity and optical properties of bodies on the radiation frequency. We establish the existence and uniqueness of a weak solution. We prove the comparison theorem and derive a priori estimates for weak solutions and obtain a regularity result.