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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2021, Volume 25, Number 3, Pages 423–434
DOI: https://doi.org/10.14498/vsgtu1859 (Mi vsgtu1859) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Differential Equations and Mathematical Physics

The second initial-boundary value problem with integral displacement for second-order hyperbolic and parabolic equations

A. I. Kozhanovab, A. V. Dyuzhevab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation
b Samara State Technical University, Samara, 443100, Russian Federation
Full-text PDF (923 kB) Citations (7)
(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu1859
Abstract: In this paper, we study the solvability of some non-local analogs of the second initial-boundary value problem for multidimensional hyperbolic and parabolic equations of the second order. We prove the existence and uniqueness theorems of regular solutions (which have all Sobolev generalized derivatives that are summable with a square and are included in the equation). Some generalization and amplification of the obtained results are also given.
Keywords: hyperbolic equations, parabolic equations, integral boundary conditions, nonlocal problems, integral conditions, regular solutions, uniqueness, existence.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0778-2020-0005
The work was carried out with the financial support of the Ministry of education and science of the Russian Federation in the framework of state task no. 0778–2020–0005.
Received: March 26, 2021
Revised: May 20, 2021
Accepted: August 25, 2021
First online: September 7, 2021
Bibliographic databases:
Document Type: Article
UDC: 517.953
MSC: 35M13
Language: Russian
Citation: A. I. Kozhanov, A. V. Dyuzheva, “The second initial-boundary value problem with integral displacement for second-order hyperbolic and parabolic equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 25:3 (2021), 423–434
Citation in format AMSBIB
\Bibitem{KozDyu21}
\by A.~I.~Kozhanov, A.~V.~Dyuzheva
\paper The second initial-boundary value problem with integral displacement for second-order hyperbolic and parabolic equations
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2021
\vol 25
\issue 3
\pages 423--434
\mathnet{http://mi.mathnet.ru/vsgtu1859}
\crossref{https://doi.org/10.14498/vsgtu1859}
\zmath{https://zbmath.org/?q=an:7499952}
\elib{https://elibrary.ru/item.asp?id=46801514}
\edn{https://elibrary.ru/ZAKEGT}
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  • https://www.mathnet.ru/eng/vsgtu/v225/i3/p423
    Erratum
    This publication is cited in the following 7 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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