Problem of radiation heat exchange with boundary conditions of the Cauchy type

Unique solvability of a stationary radiative‐conductive heat transfer problem in a system consisting of an absolutely black body and several semitransparent bodies

“…In the past 30 years, a large number of papers have been devoted to the solvability of complex heat transfer problems in radiation‐opaque or radiation‐semitransparent materials (cf. other works 16–47,48–64 ). Note that, in the literature, 46–51,53,59–64 the radiation transfer equation is changed by its diffusion P 1 approximation.…”

Mathematical modeling of complex heat transfer in the context of the endovenous laser ablation

“…Theoretical and numerical aspects of various reaction-diffusion problems are discussed in works IOP Publishing doi:10.1088/1742-6596/2514/1/012006 2 [3,4,5,6]. Nonlinear reaction-diffusion systems of heat exchange taking into account the radiation effects are considered in [7,8]. In papers [9,10,11], EVLA process is simulated by the heat transfer equation of the reaction-diffusion type, and to calculate the density of the absorbed energy of radiation, an explicit formula for the intensity of radiation induced by a point source in infinite homogeneous medium is applied.…”