On the Solvability of a Nonstandard Nonlinear Boundary Value Problem Encountered in Homogenizing a Complex Heat Transfer Problem
DOI:
https://doi.org/10.24160/1993-6982-2025-6-199-205Keywords:
radiative-conductive heat transfer, radiative heat transfer conditions, asymptotic approximations, nonlinear boundary value problemAbstract
In numerous physical and engineering applications, the problem of studying radiative-conductive heat transfer processes is encountered. Thermal radiation exhibits nonlinear dependence on temperature, and its propagation is described by integro-differential equations. This leads to various non-standard nonlinear nonlocal boundary value problems.
The article continues a series of works addressing the construction and analysis of special discrete, semi-discrete, and asymptotic approximations of complex (radiative-conductive) heat transfer problems in small-scale structures consisting of a large number of heat-conductive elements separated by vacuum interlayers or cavities.
A non-standard nonlinear boundary value problem that is encountered in homogenizing certain complex heat transfer problems in periodic structures is considered. The existence of a solution and a comparison principle are proven, from which the uniqueness of the problem solution follows.
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Для цитирования: Амосов А.А., Крымов Н.Е. О разрешимости одной нестандартной нелинейной краевой задачи, возникающей при гомогенизации задачи сложного теплообмена // Вестник МЭИ. 2025. № 6. С. 199—205. DOI: 10.24160/1993-6982-2025-6-199-205
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Результаты работы получены в рамках выполнения государственного задания Министерствa науки и высшего образования Российской Федерации (проект № FSWF-2023-0012)
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Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
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21. Amosov A.A. Asymptotic Approximations for the Stationary Radiative-conductive Heat Transfer Problem in a Two-dimensional System of Plates. Russ. J. Numer. Anal. Math. Model. 2017;32(3):173—185.
22. Amosov A.A., Krymov N.E. On a Nonstandard Boundary Value Problem Arising in Homogenization of Complex Heat Transfer Problems. J. Math. Sci. 2020;244(3):357—377.
23. Amosov A.A., Krymov N.E. Discrete and Asymptotical Approximations for One Stationary Radiative-conductive Heat Transfer Problem. Russ. J. Numer. Anal. Math. Model. 2020;35(3):127—141.
24. Amosov A.A., Krymov N.E. Error Estimate for Discrete Approximation of the Radiative-conductive Heat Transfer Problem in a System of Absolutely Black Rods. J. Math. Sci. 2020;251(6):773—786.
25. Amosov A.A., Krymov. N.E. On a Nonlinear Initial-boundary Value Problem with Venttsel Type Boundary Conditions Arizing in Homogenization of Complex Heat Transfer Problems. Mathematics. 2022;1890(10):1—23.
26. Amosov A.A., Krymov N.E. Justification of Discrete and Asymptotic Approximations for the Complex Heat Transfer Problem. J. Math. Sci. 2022;264(5):489—513
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For citation: Amosov A.A., Krymov N.E. On the Solvability of a Nonstandard Nonlinear Boundary Value Problem Encountered in Homogenizing a Complex Heat Transfer Problem. Bulletin of MPEI. 2025;6:199—205. (in Russian). DOI: 10.24160/1993-6982-2025-6-199-205
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The Results were Obtained as Part of the State Assignment of the Ministry of Science and Higher Education of the Russian Federation (Project No. FSWF-2023-0012)
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Conflict of interests: the authors declare no conflict of interest
