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Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya, 2023, Volume 29, Issue 3, Pages 8–17
DOI: https://doi.org/10.18287/2541-7525-2023-29-3-8-17 (Mi vsgu706) 		 
Mathematics

A non-local problem with integral conditions of the first kind for the string vibration equation

Y. S. Buntova

Samara National Research University, Samara, Russian Federation
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DOI: https://doi.org/10.18287/2541-7525-2023-29-3-8-17
Abstract: In this article, we consider a problem with nonlocal integral conditions of the 1st kind for the one-dimensional wave equation. The kernels of the integral conditions depend on both spatial and time variables. In order to study this problem we reduce first the integral conditions of the 1st kind to the integral conditions of the 2nd kind. Under certain additional assumptions these nonlocal conditions are equivalent. Obtained restriction on input data enable to show uniqurness of generalized solution to the problem.
Keywords: hyperbolic equation, nonlocal problem, integral conditions, generalized solution.
Received: 24.07.2023
Revised: 31.08.2023
Accepted: 30.10.2023
Document Type: Article
UDC: 517.95
Language: Russian
Citation: Y. S. Buntova, “A non-local problem with integral conditions of the first kind for the string vibration equation”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 29:3 (2023), 8–17
Citation in format AMSBIB
\Bibitem{Bun23}
\by Y.~S.~Buntova
\paper A non-local problem with integral conditions of the first kind for the string vibration equation
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2023
\vol 29
\issue 3
\pages 8--17
\mathnet{http://mi.mathnet.ru/vsgu706}
\crossref{https://doi.org/10.18287/2541-7525-2023-29-3-8-17}
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    		Вестник Самарского государственного университета. Естественнонаучная серия
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