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 Eurasian Math. J., 2015, Volume 6, Number 4, Pages 19–28 (Mi emj207)

On conditions of the solvability of nonlocal multi-point boundary value problems for quasi-linear systems of hyperbolic equations

A. T. Assanovaa, A. E. Imanchievb

a Department of Differential Equations, Institute of Mathematics and Mathematical Modeling MES RK, 125 Pushkin St., 050010 Almaty, Kazakhstan
b Faculty of Physics and Mathematics, K. Zhubanov Aktobe Regional State University, 34 A. Moldagulova St., Aktobe 030000, Kazakhstan

Abstract: A nonlocal multi-point boundary value problem for a system of quasi-linear hyperbolic equations is investigated. Based on the results for linear problems coefficient conditions are established ensuring the existence of classical solutions to nonlocal multi-point boundary value problem for a system of quasi-linear hyperbolic equations, and algorithms of finding these solutions are suggested.

Keywords and phrases: nonlocal problem, multi-point condition, quasi-linear hyperbolic equation, solvability.

 Funding Agency Grant Number Ministry of Education and Science of the Republic of Kazakhstan 0822/ΓΦ 4 This work supported by Grant No. 0822/ΓΦ 4 (2015-2017) of the Science Committee of the Ministry of education and Science of the Republic of Kazakhstan.

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MSC: 35L20, 35L55, 34B08, 35L72
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Citation: A. T. Assanova, A. E. Imanchiev, “On conditions of the solvability of nonlocal multi-point boundary value problems for quasi-linear systems of hyperbolic equations”, Eurasian Math. J., 6:4 (2015), 19–28

Citation in format AMSBIB
\Bibitem{AssIma15} \by A.~T.~Assanova, A.~E.~Imanchiev \paper On conditions of the solvability of nonlocal multi-point boundary value problems for quasi-linear systems of hyperbolic equations \jour Eurasian Math. J. \yr 2015 \vol 6 \issue 4 \pages 19--28 \mathnet{http://mi.mathnet.ru/emj207} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380173800002} 

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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. A. T. Assanova, A. E. Imanchiev, Zh. M. Kadirbayeva, “On the unique solvability of a multi-point problem for system of the loaded differential equations hyperbolic type”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 2:312 (2017), 12–17
2. A. T. Assanova, H. A. Ashirbaev, A. P. Sabalakhova, “On the nonlocal problem for a system of the partial integro-differential equations of hyperbolic type”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 4:314 (2017), 11–18
3. A. T. Assanova, E. A. Bakirova, Zh. M. Kadirbayeva, “Method for solving the periodic problem for an impulsive system of hyperbolic integro-differential equations”, International Conference Functional Analysis in Interdisciplinary Applications FAIA 2017, AIP Conf. Proc., 1880, eds. T. Kalmenov, M. Sadybekov, Amer. Inst. Phys., 2017, UNSP 040004
4. A. T. Assanova, Zh. M. Kadirbayeva, “Periodic problem for an impulsive system of the loaded hyperbolic equations”, Electron. J. Differ. Equ., 2018, 72
5. 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
6. A. T. Assanova, A. A. Boichuk, Z. S. Tokmurzin, “On the initial-boundary value problem for system of the partial differential equations of fourth order”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 1:323 (2019), 14–21
7. A. T. Assanova, Z. S. Tokmurzin, “A nonlocal multipoint problem for a system of fourth-order partial differential equations”, Eurasian Math. J., 11:3 (2020), 8–20
8. A. T. Assanova, Zh. K. Dzhobulaeva, A. E. Imanchiyev, “A multi-point initial problem for a non-classical system of a partial differential equations”, Lobachevskii J. Math., 41:6, SI (2020), 1031–1042
9. A. T. Assanova, A. D. Abildayeva, A. P. Sabalakhova, “An initial-boundary value problem for a higher-order partial differential equation”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 2:330 (2020), 133–141
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