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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 204, Pages 146–159
DOI: https://doi.org/10.36535/0233-6723-2022-204-146-159 (Mi into950) 		 
On the first initial-boundary-value problem of heat conduction in a domain with curvilinear lateral boundaries

K. D. Fedorovab

a Moscow Center for Fundamental and Applied Mathematics
b Lomonosov Moscow State University
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DOI: https://doi.org/10.36535/0233-6723-2022-204-146-159
Abstract: We consider the first initial-boundary-value problem for the heat equation in a bounded domain $\Omega$ with curvilinear lateral boundaries. Using the method of boundary integral equations, we prove the existence of a solution to this problem in the class $C^{2,1}_{x,t}(\overline{\Omega})$.
Keywords: first initial-boundary-value problem, parabolic equation, nonsmooth lateral boundary, method of boundary integral equations.
Document Type: Article
UDC: 517.956.4
MSC: 35A01
Language: Russian
Citation: K. D. Fedorov, “On the first initial-boundary-value problem of heat conduction in a domain with curvilinear lateral boundaries”, Proceedings of the Voronezh spring mathematical school  "Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI". Voronezh, May 3-9, 2020, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 204, VINITI, Moscow, 2022, 146–159
Citation in format AMSBIB
\Bibitem{Fed22}
\by K.~D.~Fedorov
\paper On the first initial-boundary-value problem of heat conduction in a domain with curvilinear lateral boundaries
\inbook Proceedings of the Voronezh spring mathematical school 
"Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI".
Voronezh, May 3-9, 2020
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 204
\pages 146--159
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into950}
\crossref{https://doi.org/10.36535/0233-6723-2022-204-146-159}
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