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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 5, Pages 856–863
DOI: https://doi.org/10.31857/S0044466923050162 (Mi zvmmf11560) 		 
Mathematical physics

The problem of complex heat transfer with Cauchy-type conditions on a part of the boundary

P. R. Meseneva, A. Yu. Chebotarevbc

a Far Eastern Center for Mathematical Research, Far East Federal University, 690922, Vladivostok, Russia
b Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia
c Amur State University, 675027, Blagoveshchensk, Amur oblast, Russia
DOI: https://doi.org/10.31857/S0044466923050162
Abstract: The paper considers a boundary value problem for stationary equations of complex heat transfer with an undetermined boundary condition for the radiation intensity on a part of the boundary and an overdetermined condition on another part of the boundary. An optimization method for solving this problem is proposed, and an analysis of the corresponding problem of boundary optimal control is presented. It is shown that the sequence of solutions of extremum problems converges to the solution of a problem with Cauchy-type conditions. The efficiency of the algorithm is illustrated by numerical examples.
Key words: radiative-conductive heat transfer equations, diffusion approximation, boundary value problem with Cauchy-type conditions, optimal control problem.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00113
Ministry of Education and Science of the Russian Federation АААА-А20-120120390006-0
Ministry of Science and Higher Education of the Russian Federation 122082400001-8
This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00113); the Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences (IAM FEB RAS) (project no. АААА-А20-120120390006-0); and the Ministry of Education and Science of the Russian Federation (project no. 122082400001-8).
Received: 09.08.2022
Revised: 16.11.2022
Accepted: 02.02.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 5, Pages 897–904
DOI: https://doi.org/10.1134/S0965542523050135
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: P. R. Mesenev, A. Yu. Chebotarev, “The problem of complex heat transfer with Cauchy-type conditions on a part of the boundary”, Zh. Vychisl. Mat. Mat. Fiz., 63:5 (2023), 856–863; Comput. Math. Math. Phys., 63:5 (2023), 897–904
Citation in format AMSBIB
\Bibitem{MesChe23}
\by P.~R.~Mesenev, A.~Yu.~Chebotarev
\paper The problem of complex heat transfer with Cauchy-type conditions on a part of the boundary
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 5
\pages 856--863
\mathnet{http://mi.mathnet.ru/zvmmf11560}
\crossref{https://doi.org/10.31857/S0044466923050162}
\elib{https://elibrary.ru/item.asp?id=53738581}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 5
\pages 897--904
\crossref{https://doi.org/10.1134/S0965542523050135}
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