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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 10, Pages 32–44 (Mi ivm8743)  
This article is cited in 39 scientific papers (total in 39 papers)

A nonlocal problem for a hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels

L. S. Pul'kina

Chair of Equations of Mathematical Physics, Samara State University, Samara, Russia
Full-text PDF (193 kB) Citations (39)
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Abstract: We consider a nonlocal problem with integral conditions of the 1st kind. The main goal is to prove the unique solvability of this problem under the assumption that kernels of nonlocal conditions depend both on spatial and time variables. To this end we propose a technique based on the proved equivalence between the nonlocal problem with integral conditions of the 1st kind and a nonlocal problem with integral conditions of the second kind in a special form. We formulate requirements to the initial data guaranteeing the unique existence of a generalized solution to the stated problem.
Keywords: hyperbolic equation, nonlocal problem, integral conditions, generalized solution.
Received: 08.08.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 10, Pages 26–37
DOI: https://doi.org/10.3103/S1066369X12100039
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: L. S. Pul'kina, “A nonlocal problem for a hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 10, 32–44; Russian Math. (Iz. VUZ), 56:10 (2012), 26–37
Citation in format AMSBIB
\Bibitem{Pul12}
\by L.~S.~Pul'kina
\paper A nonlocal problem for a~hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 10
\pages 32--44
\mathnet{http://mi.mathnet.ru/ivm8743}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3137057}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 10
\pages 26--37
\crossref{https://doi.org/10.3103/S1066369X12100039}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84869422481}
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    • This publication is cited in the following 39 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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