Abstract
The paper is devoted to a nonstationary initial–boundary value problem governing complex heat exchange in a convex semitransparent body containing several absolutely black inclusions. The existence and uniqueness of a weak solution to this problem are proven herein. In addition, the stability of solutions with respect to data, a comparison theorem and the results of improving the properties of solutions with an increase in the summability of the data were established. All results are global in terms of time and data.
Highlights
The paper is devoted to a nonstationary initial–boundary value problem governing complex heat exchange in a convex semitransparent body containing several absolutely black inclusions
To describe the nonstationary process of radiative–conductive heat transfer, a system consisting of two heat equations and radiative transfer equation is used:
The author continues to construct a mathematical theory of complex heat transfer problems
Summary
Problem in a Semitransparent Body with Absolutely Black Inclusions. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The solvability of various statements of complex (radiative–conductive) heat exchange problems in systems consisting either only of radiation-opaque bodies or only of radiation-semitransparent bodies has been studied in sufficient detail. The problems of radiative–conductive heat exchange in systems consisting of both radiation-opaque and of radiation-semitransparent bodies remain to date unexplored. This specific area of study, to the best of the author’s knowledge, has only been the subject of the following articles: [64–66]. The existence and uniqueness of a weak solution to a nonstationary boundary value problem governing radiative–conductive heat transfer in a semitransparent body containing several absolutely black inclusions were proven. In (8), J∗ denotes the intensity of external radiation b incident on ∂ G
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