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Izvestiya: Mathematics, 2017, Volume 81, Issue 3, Pages 542–567
DOI: https://doi.org/10.1070/IM8442 (Mi im8442) 		 
This article is cited in 11 scientific papers (total in 11 papers)

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

N. A. Zhuraa, A. P. Soldatovb

a P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow
b National Research University "Belgorod State University"
English version PDF (377 kB) Citations (11)
References:
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DOI: https://doi.org/10.1070/IM8442
Abstract: We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.
Keywords: strictly hyperbolic first-order systems of differential equations, two-dimensional admissible domains, boundary-value problems, shift operator, functional operator, estimate for the spectral radius of a functional operator.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan 3492.ГФ4
This paper was written with the support of International Project (3492.GF4) of the Ministry of Education and Science of Kazakhstan Republic.
Received: 09.09.2015
Revised: 04.05.2016
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2017, Volume 81, Issue 3, Pages 83–108
DOI: https://doi.org/10.4213/im8442
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35F45, 39B42, 47A10, 47B33
Language: English
Original paper language: Russian
Citation: N. A. Zhura, A. P. Soldatov, “A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain”, Izv. RAN. Ser. Mat., 81:3 (2017), 83–108; Izv. Math., 81:3 (2017), 542–567
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:439
    Russian version PDF:64
    English version PDF:8
    References:61
    First page:49
     
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