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 Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 5, Pages 11–25 (Mi ivm9233)

Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle

A. T. Assanova

Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, 125 Pushkin str., Almaty, 050010 Republic of Kazakhstan

Abstract: We consider a nonlocal problem with integral conditions for a system of hyperbolic equations in rectangular domain. We investigate the questions of existence of unique classical solution to the problem under consideration and approaches of its construction. Sufficient conditions of unique solvability to the investigated problem are established in the terms of initial data. The nonlocal problem with integral conditions is reduced to an equivalent problem consisting of the Goursat problem for the system of hyperbolic equations with functional parameters and functional relations. We propose algorithms for finding a solution to the equivalent problem with functional parameters on the characteristics and prove their convergence. We also obtain the conditions of a unique solvability to the boundary-value problem with integral condition for the system of an ordinary differential equations. As an example, we consider the nonlocal boundary-value problem with integral conditions for two-dimensional system of hyperbolic equations.

Keywords: system of hyperbolic equations, nonlocal problem, integral condition, solvability, algorithm.

 Funding Agency Grant Number Ministry of Education and Science of the Republic of Kazakhstan 0822/ÃÔ4

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:5, 7–20

Bibliographic databases:

UDC: 517.956

Citation: A. T. Assanova, “Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 5, 11–25; Russian Math. (Iz. VUZ), 61:5 (2017), 7–20

Citation in format AMSBIB
\Bibitem{Ass17} \by A.~T.~Assanova \paper Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2017 \issue 5 \pages 11--25 \mathnet{http://mi.mathnet.ru/ivm9233} \transl \jour Russian Math. (Iz. VUZ) \yr 2017 \vol 61 \issue 5 \pages 7--20 \crossref{https://doi.org/10.3103/S1066369X17050024} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000408843700002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85018417727} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. O. M. Kechina, “O razreshimosti nelokalnoi zadachi dlya uravneniya tretego poryadka”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 1, 15–20
2. Assanova A.T., “Solvability of a Nonlocal Problem For a Hyperbolic Equation With Integral Conditions”, Electron. J. Differ. Equ., 2017, 170
3. A. T. Assanova, B. Zh. Alikhanova, K. Zh. Nazarova, “Well-posedness of a nonlocal problem with integral conditions for third order system of the partial differential equations”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 5:321 (2018), 33–41
4. A. T. Asanova, “O reshenii nachalno-kraevoi zadachi dlya sistemy differentsialnykh uravnenii v chastnykh proizvodnykh tretego poryadka”, Izv. vuzov. Matem., 2019, no. 4, 15–26
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