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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 4, Pages 870–883
DOI: https://doi.org/10.33048/smzh.2022.63.413 (Mi smj7700) 		 
Existence and uniqueness of the solution to a degenerate third boundary value problem for a multidimensional parabolic equation

A. I. Kozhanova, V. V. Shubinb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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DOI: https://doi.org/10.33048/smzh.2022.63.413
Abstract: We study the well-posedness of a third boundary value problem for a multidimensional parabolic equation in the case when the coefficient of the conormal derivative vanishes at some points. We show that under some conditions on the sign of this coefficient there exists nonexistence or nonuniqueness of a solution in the conventional anisotropic Sobolev space. Using the regularization method, we prove existence and uniqueness theorems for the regular solution in suitable weighted spaces.
Keywords: parabolic equation, third boundary value problem, degeneration, existence, uniqueness.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-281
The work is supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2022–281 on April 5, 2022 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 23.11.2021
Revised: 05.01.2022
Accepted: 10.02.2022
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 4, Pages 723–734
DOI: https://doi.org/10.1134/S0037446622040139
Document Type: Article
UDC: 517.95
Language: Russian
Citation: A. I. Kozhanov, V. V. Shubin, “Existence and uniqueness of the solution to a degenerate third boundary value problem for a multidimensional parabolic equation”, Sibirsk. Mat. Zh., 63:4 (2022), 870–883; Siberian Math. J., 63:4 (2022), 723–734
Citation in format AMSBIB
\Bibitem{KozShu22}
\by A.~I.~Kozhanov, V.~V.~Shubin
\paper Existence and uniqueness of the solution to a~degenerate third boundary value problem for a~multidimensional parabolic equation
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 4
\pages 870--883
\mathnet{http://mi.mathnet.ru/smj7700}
\crossref{https://doi.org/10.33048/smzh.2022.63.413}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 4
\pages 723--734
\crossref{https://doi.org/10.1134/S0037446622040139}
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