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 Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 10, Pages 41–52 (Mi ivm9163)

A problem with a nonlocal with respect to time condition for multidimensional hyperbolic equations

L. S. Pul'kinaa, A. E. Savenkovab

a Samara National Research University named after academician S. P. Korolyov, 34 Moskovskoe Highway, Samara, 443086 Russia
b Samara Technical State University, 244 Molodogvardeiskaya str., Samara, 443100 Russia

Abstract: We study the boundary-value problem for hyperbolic equation with nonlocal with respect to time-variable condition in integral form. We obtain sufficient conditions for the unique solvability of the nonlocal problem. The proof is based on possibility to reduce a nonlocal condition of the first kind to the second kind one. This allows to reduce the nonlocal problem to an operator equation. We show that unique solvability of the operator equation implies the existence of a unique solution to the posed problem.

Keywords: hyperbolic equation, nonlocal problem, integral conditions, generalized solution.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:10, 33–43

Bibliographic databases:

UDC: 517.956
Revised: 28.10.2015

Citation: L. S. Pul'kina, A. E. Savenkova, “A problem with a nonlocal with respect to time condition for multidimensional hyperbolic equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 10, 41–52; Russian Math. (Iz. VUZ), 60:10 (2016), 33–43

Citation in format AMSBIB
\Bibitem{PulSav16} \by L.~S.~Pul'kina, A.~E.~Savenkova \paper A~problem with a~nonlocal with respect to time condition for multidimensional hyperbolic equations \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2016 \issue 10 \pages 41--52 \mathnet{http://mi.mathnet.ru/ivm9163} \transl \jour Russian Math. (Iz. VUZ) \yr 2016 \vol 60 \issue 10 \pages 33--43 \crossref{https://doi.org/10.3103/S1066369X16100066} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000409307300006} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84988838011} 

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• http://mi.mathnet.ru/eng/ivm/y2016/i10/p41

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. K. Urinov, Sh. T. Nishonova, “A Problem with Integral Conditions for an Elliptic-Parabolic Equation”, Math. Notes, 102:1 (2017), 68–80
2. S. Z. Dzhamalov, “The nonlocal boundary value problem with constant coefficients for the mixed type of equation of the first kind in a plane”, Malays. J. Math. Sci., 12:1 (2018), 49–62
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