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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 8, Pages 56–68
DOI: https://doi.org/10.26907/0021-3446-2022-8-56-68 (Mi ivm9802) 		 
Multiperiodic solution of the initial-boundary value problem for integro-differential equation of parabolic type

Zh. A. Sartabanova, G. M. Aitenovab, G. A. Abdikalikovaa

a K.Zhubanov Aktobe Regional University, Aktobe, 34 A. Moldagulova Ave., Aktobe, 030000 Republic of Kazakhstan
b M. Utemisov West-Kazakhstan University, 162 N. Nazarbaev Ave., Uralsk, 090000 Republic of Kazakhstan
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DOI: https://doi.org/10.26907/0021-3446-2022-8-56-68
Abstract: The initial-boundary value problem for an integro-differential equation of parabolic type with a differentiation operator with respect to multidimensional time is investigated. A fundamental solution is constructed and some of its properties associated with multiperiodicity in time and diagonal periodicity in space variables are found. An estimate is obtained for the fundamental solution of an integro-differential equation. The existence and uniqueness of multiperiodic solutions of the boundary value problem with respect to all arguments are established and some basic properties of the sought solutions are found.
Keywords: integro-differential, multidimensional time, parabolicity, operator series, multiperiodicity, initial-boundary.
Received: 30.10.2021
Revised: 17.03.2022
Accepted: 29.06.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 8, Pages 46–55
DOI: https://doi.org/10.3103/S1066369X22080084
Document Type: Article
UDC: 517.95
Language: Russian
Citation: Zh. A. Sartabanov, G. M. Aitenova, G. A. Abdikalikova, “Multiperiodic solution of the initial-boundary value problem for integro-differential equation of parabolic type”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 8, 56–68; Russian Math. (Iz. VUZ), 66:8 (2022), 46–55
Citation in format AMSBIB
\Bibitem{SarAitAbd22}
\by Zh.~A.~Sartabanov, G.~M.~Aitenova, G.~A.~Abdikalikova
\paper Multiperiodic solution of the initial-boundary value problem for integro-differential equation of parabolic type
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 8
\pages 56--68
\mathnet{http://mi.mathnet.ru/ivm9802}
\crossref{https://doi.org/10.26907/0021-3446-2022-8-56-68}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 8
\pages 46--55
\crossref{https://doi.org/10.3103/S1066369X22080084}
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