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Unique solvability of a stationary radiative‐conductive heat transfer problem in a system consisting of an absolutely black body and several semitransparent bodies
Author(s) -
Amosov Andrey
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7439
Subject(s) - radiative transfer , mathematics , thermal radiation , boundary value problem , mathematical analysis , heat transfer , intensity (physics) , radiation , mechanics , physics , thermodynamics , optics
We consider a stationary boundary value problem describing a radiative‐conductive heat transfer in a system consisting of one absolutely black body and several semitransparent bodies. 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.