On nonlocal integro-differential boundary value problems for multidimensional pseudoparabolic equations
https://doi.org/10.25587/2411-9326-2024-3-39-52
Abstract
The solvability of the initial-boundary value problem for linear integrodifferential equations with a condition on the lateral boundary that connects the values of the solution or the conormal derivative of the solution with the values of some integral operator of the solution is investigated. Theorems of existence and uniqueness of regular solutions are proved. The systematic study of nonlocal boundary value problems – the problems of finding periodic solutions to elliptic equations – was initiated by Bitsadze and Samarskii in 1969. Note also the studies for pseudoparabolic and pseudohyperbolic thirdorder equations with an integral condition on the lateral boundary. Great contributions to the development of the theory of nonlocal problems for differential equations of various classes were made by the monographs of Skubachevsky in 1997, Nakhushev in 2006 and 2012, and Kozhanov in 2024.
About the Author
N. S. Popov
Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics
Russian Federation
Russian Federation
Nikolay S. Popov
48 Kulakovsky Street, Yakutsk 677000
References
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Review
For citations:
Popov N.S. On nonlocal integro-differential boundary value problems for multidimensional pseudoparabolic equations. Mathematical notes of NEFU. 2024;31(3):39-52. (In Russ.) https://doi.org/10.25587/2411-9326-2024-3-39-52
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