Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 223, Pages 14–23
DOI: https://doi.org/10.36535/0233-6723-2023-223-14-23 (Mi into1151) 		 
On discrete boundary-value problems in a quarter plane

V. B. Vasilev (Vasilyev), A. A. Khodyreva

National Research University "Belgorod State University"
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DOI: https://doi.org/10.36535/0233-6723-2023-223-14-23
Abstract: We consider a discrete elliptic pseudodifferential equation in a quadrant and the corresponding discrete boundary-value problem. Conditions for the solvability of the discrete boundary-value problem in discrete analogs of the Sobolev–Slobodetskii spaces are described. The discrete solution is compared with the solution of the corresponding continuum boundary-value problem depending on the discretization parameter.
Keywords: discrete pseudodifferential operator, two-dimensional periodic Riemann problem, periodic wave factorization, analyticity, solvability.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FZWG-2020-0029
This work was supported by the Ministry of Science and Higher Education (project No. FZWG-2020-0029).
Document Type: Article
UDC: 517.954, 517.983
MSC: 35S15, 47B38
Language: Russian
Citation: V. B. Vasilev (Vasilyev), A. A. Khodyreva, “On discrete boundary-value problems in a quarter plane”, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 223, VINITI, Moscow, 2023, 14–23
Citation in format AMSBIB
\Bibitem{VasKho23}
\by V.~B.~Vasilev~(Vasilyev), A.~A.~Khodyreva
\paper On discrete boundary-value problems in a~quarter plane
\inbook Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 223
\pages 14--23
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1151}
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