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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 10, Pages 41–52 (Mi ivm9163)  
This article is cited in 14 scientific papers (total in 14 papers)

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
Full-text PDF (200 kB) Citations (14)
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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.
Received: 07.10.2014
Revised: 28.10.2015
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 10, Pages 33–43
DOI: https://doi.org/10.3103/S1066369X16100066
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
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
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\pages 41--52
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\issue 10
\pages 33--43
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    • This publication is cited in the following 14 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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