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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2022, Volume 26, Number 2, Pages 380–395
DOI: https://doi.org/10.14498/vsgtu1904 (Mi vsgtu1904) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Short Communication
Differential Equations and Mathematical Physics

A problem with nonlocal conditions for a one-dimensional parabolic equation

A. B. Beylina, A. V. Bogatovb, L. S. Pulkinab

a Samara State Technical University, Samara, 443100, Russain Federation
b Samara National Research University, Samara, 443086, Russian Federation
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DOI: https://doi.org/10.14498/vsgtu1904
Abstract: In present paper, we consider a problem with nonlocal conditions for parabolic equation and show that there exists a unique weak solution in Sobolev space. The main tool to prove the existence of a unique weak solution to the problem is a priori estimates derived by authors. We also note a connection between Steklov nonlocal conditions and first kind integral conditions. This connection enables interpret the problem under consideration as a problem with perturbed Steklov nonlocal conditions. Obtained results may be useful for certain class of problems including inverse problems.
Keywords: parabolic equation, boundary-value problem, nonlocal conditions, generalized solution; Sobolev spaces.
Received: January 24, 2022
Revised: March 2, 2022
Accepted: May 23, 2022
First online: May 26, 2022
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35L20, 35B45, 35D30
Language: Russian
Citation: A. B. Beylin, A. V. Bogatov, L. S. Pulkina, “A problem with nonlocal conditions for a one-dimensional parabolic equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 26:2 (2022), 380–395
Citation in format AMSBIB
\Bibitem{BeyBogPul22}
\by A.~B.~Beylin, A.~V.~Bogatov, L.~S.~Pulkina
\paper A problem with nonlocal conditions for a one-dimensional parabolic equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2022
\vol 26
\issue 2
\pages 380--395
\mathnet{http://mi.mathnet.ru/vsgtu1904}
\crossref{https://doi.org/10.14498/vsgtu1904}
\edn{https://elibrary.ru/USPHOK}
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  • https://www.mathnet.ru/eng/vsgtu/v226/i2/p380
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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