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Matematicheskie Zametki, 2022, Volume 111, Issue 5, Pages 778–794
DOI: https://doi.org/10.4213/mzm13201 (Mi mzm13201) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Approximation of Solutions to the Heat Equation in the Lebesgue Class $L^2$ by More Regular Solutions

A. A. Shlapunovab

a Siberian Federal University, Krasnoyarsk
b University of Science and Technology "Sirius", Sochi
Full-text PDF (579 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm13201
Abstract: A criterion for the approximability of all solutions of the heat equation in a bounded cylindrical domain that belong to the Lebesgue class by more regular (e.g., Sobolev) solutions of the same equation in a bounded cylindrical domain with larger base is obtained. Namely, the complement of the smaller base to the larger one must have no (nonempty connected) compact components. As an important corollary, we prove a theorem on the existence of a doubly orthogonal basis for the corresponding pair of Hilbert spaces.
Keywords: heat equation, approximation theorem.
Funding agency Grant number
Научно-технологический университет «Сириус»
This work was supported by Sirius University of Science and Technology in the framework of the scientific project “Spectral and functional inequalities of mathematical physics and their applications.”
Received: 01.07.2021
Published: 23.04.2022
English version:
Mathematical Notes, 2022, Volume 111, Issue 5, Pages 782–794
DOI: https://doi.org/10.1134/S0001434622050121
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. A. Shlapunov, “On the Approximation of Solutions to the Heat Equation in the Lebesgue Class $L^2$ by More Regular Solutions”, Mat. Zametki, 111:5 (2022), 778–794; Math. Notes, 111:5 (2022), 782–794
Citation in format AMSBIB
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\by A.~A.~Shlapunov
\paper On the Approximation of Solutions to the Heat Equation in the Lebesgue Class $L^2$ by More Regular Solutions
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 5
\pages 778--794
\mathnet{http://mi.mathnet.ru/mzm13201}
\crossref{https://doi.org/10.4213/mzm13201}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4461306}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 5
\pages 782--794
\crossref{https://doi.org/10.1134/S0001434622050121}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85132799823}
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    • This publication is cited in the following 2 articles:
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