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Matematicheskie Zametki, 2024, Volume 115, Issue 2, Pages 230–244
DOI: https://doi.org/10.4213/mzm13877 (Mi mzm13877) 		 
On the Well-Posedness of an Initial–Boundary Value Problem for a Degenerate Heat Equation

A. R. Zaynullova, K. B. Sabitovba

a Sterlitamak branch of the Ufa University of Science and Technology
b Mavlyutov Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences
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DOI: https://doi.org/10.4213/mzm13877
Abstract: The well-posedness of an initial–boundary value problem for a model parabolic equation with two power-law degeneration lines is studied. Two initial–boundary value problems depending on the degeneracy exponents are stated, and uniqueness and existence theorems are proved. The solutions of these problems are constructed in closed form.
Keywords: parabolic equation with two power degeneration lines, initial–boundary value problem, uniqueness, existence, series, integral representation.
Received: 08.01.2023
English version:
Mathematical Notes, 2024, Volume 115, Issue 2, Pages 192–204
DOI: https://doi.org/10.1134/S0001434624010188
Bibliographic databases:
Document Type: Article
UDC: 519.65
PACS: 02.30.Jr
MSC: 35K05
Language: Russian
Citation: A. R. Zaynullov, K. B. Sabitov, “On the Well-Posedness of an Initial–Boundary Value Problem for a Degenerate Heat Equation”, Mat. Zametki, 115:2 (2024), 230–244; Math. Notes, 115:2 (2024), 192–204
Citation in format AMSBIB
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\by A.~R.~Zaynullov, K.~B.~Sabitov
\paper On the Well-Posedness of an Initial--Boundary Value Problem for a Degenerate Heat Equation
\jour Mat. Zametki
\yr 2024
\vol 115
\issue 2
\pages 230--244
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\crossref{https://doi.org/10.4213/mzm13877}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4734355}
\transl
\jour Math. Notes
\yr 2024
\vol 115
\issue 2
\pages 192--204
\crossref{https://doi.org/10.1134/S0001434624010188}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85190840081}
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