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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 8, Pages 3–23
DOI: https://doi.org/10.26907/0021-3446-2022-8-3-23 (Mi ivm9797) 		 
A nonlocal problem for fourth-order loaded hyperbolic equations

G. A. Abdikalikovaa, A. T. Assanovab, Sh. T. Shekerbekovac

a K. Zhubanov Aktobe Regional University, 34 A.Moldagulova Ave., Aktobe, 030000 Kazakhstan
b Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050021 Kazakhstan
c Abai Kazakh National Pedagogical University, 86 Tole bi str., Almaty, 050012 Kazakhstan
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DOI: https://doi.org/10.26907/0021-3446-2022-8-3-23
Abstract: In this paper we consider the nonlocal problem for fourth-order loaded hyperbolic equations with two independent variables. Considered problem is reduced to an equivalent problem, consisting nonlocal problem for a system of loaded hyperbolic equations of second order with functional parameters and integral relations by method introducing new unknown functions. Algorithms for finding solution to the equivalent problem are proposed. Conditions for well-posedness to the nonlocal problem for the system of loaded hyperbolic equations of second order are obtained. Conditions for the existence of unique classical solution to the nonlocal problem for fourth-order loaded hyperbolic equations are established.
Keywords: fourth-order loaded hyperbolic equation, nonlocal problem, system of loaded hyperbolic equations, problem with parameter, algorithm, solvability.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP 09258829
Received: 13.10.2021
Revised: 13.10.2021
Accepted: 23.12.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 8, Pages 1–18
DOI: https://doi.org/10.3103/S1066369X22080011
Bibliographic databases:
Document Type: Article
UDC: 517.956: 517.968
Language: Russian
Citation: G. A. Abdikalikova, A. T. Assanova, Sh. T. Shekerbekova, “A nonlocal problem for fourth-order loaded hyperbolic equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 8, 3–23; Russian Math. (Iz. VUZ), 66:8 (2022), 1–18
Citation in format AMSBIB
\Bibitem{AbdAssShe22}
\by G.~A.~Abdikalikova, A.~T.~Assanova, Sh.~T.~Shekerbekova
\paper A nonlocal problem for fourth-order loaded hyperbolic equations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 8
\pages 3--23
\mathnet{http://mi.mathnet.ru/ivm9797}
\crossref{https://doi.org/10.26907/0021-3446-2022-8-3-23}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4518162}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 8
\pages 1--18
\crossref{https://doi.org/10.3103/S1066369X22080011}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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