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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 503, Pages 64–66
DOI: https://doi.org/10.31857/S268695432202014X (Mi danma251) 		 
MATHEMATICS

Boundary problems for parabolic equations with degenerate boundary condition of the third kind

A. I. Kozhanova, A. N. Artyushina, V. V. Shubinb

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.31857/S268695432202014X
Abstract: The solvability of initial-boundary value problems for linear parabolic equations of the second order with a degenerate boundary value condition of the third kind is studied. Sufficient conditions for the existence and uniqueness of solutions are given. It is shown that the degeneration effect can lead to nonuniqueness of solutions in the space $W_2^{2,1}$.
Keywords: second-order parabolic equations, boundary value problems, degenerate boundary condition of the third kind, uniqueness and nonuniqueness of solutions, existence of solutions.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 075-15-2019-1613
This work was supported by the Mathematical Center in Akademgorodok, agreement no. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.
Presented: E. I. Moiseev
Received: 02.12.2021
Revised: 02.12.2021
Accepted: 03.02.2022
English version:
Doklady Mathematics, 2022, Volume 105, Issue 2, Pages 106–108
DOI: https://doi.org/10.1134/S1064562422020144
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: A. I. Kozhanov, A. N. Artyushin, V. V. Shubin, “Boundary problems for parabolic equations with degenerate boundary condition of the third kind”, Dokl. RAN. Math. Inf. Proc. Upr., 503 (2022), 64–66; Dokl. Math., 105:2 (2022), 106–108
Citation in format AMSBIB
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\jour Dokl. Math.
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\pages 106--108
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