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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2025, Volume 65, Number 4, Pages 460–470
DOI: https://doi.org/10.31857/S0044466925040053 (Mi zvmmf11953) 		 
Partial Differential Equations

First boundary value problem for the heat conduction equation in time-degenerate domains

A. N. Konenkovab

a Yesenin Ryazan State University, 390000, Ryazan, Russia
b Moscow Center for Fundamental and Applied Mathematics, 119991, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466925040053
Abstract: We consider the first boundary value problem in a cone with a degeneracy of the domain at the initial moment of time for the heat equation. Own functions for the problem were found. Estimations of the Green’s function are obtained. For the problem with a zero boundary function, we establish unambiguous solvability in a certain class of functions that admits a definite growth when approaching the vertex of a cone. Similar results are obtained for the cone that degenerates at the final point in time. In addition, we consider the first boundary value problem in domains that are degenerate only in terms of variables.
Key words: heat conduction equation, first boundary value problem in a cone, Green’s function, first boundary value problem in time-degenerate domains, first boundary value problem in time-degenerate domains, own functions of the first boundary value problem.
Received: 10.12.2024
Revised: 10.12.2024
Accepted: 04.02.2025
English version:
Computational Mathematics and Mathematical Physics, 2025, Volume 65, Issue 4, Pages 754–764
DOI: https://doi.org/10.1134/S0965542525700058
Bibliographic databases:
Document Type: Article
UDC: 517.954.4
Language: Russian
Citation: A. N. Konenkov, “First boundary value problem for the heat conduction equation in time-degenerate domains”, Zh. Vychisl. Mat. Mat. Fiz., 65:4 (2025), 460–470; Comput. Math. Math. Phys., 65:4 (2025), 754–764
Citation in format AMSBIB
\Bibitem{Kon25}
\by A.~N.~Konenkov
\paper First boundary value problem for the heat conduction equation in time-degenerate domains
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2025
\vol 65
\issue 4
\pages 460--470
\mathnet{http://mi.mathnet.ru/zvmmf11953}
\elib{https://elibrary.ru/item.asp?id=82358153}
\transl
\jour Comput. Math. Math. Phys.
\yr 2025
\vol 65
\issue 4
\pages 754--764
\crossref{https://doi.org/10.1134/S0965542525700058}
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