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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"
References:
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
Bibliographic databases:
Document Type: Article
UDC: 517.9
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. Math., 81:3 (2017), 542–567
Citation in format AMSBIB
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\paper A boundary-value problem for a~first-order hyperbolic system in a~two-dimensional domain
\jour Izv. Math.
\yr 2017
\vol 81
\issue 3
\pages 542--567
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Linking options:
  • https://www.mathnet.ru/eng/im8442
  • https://doi.org/10.1070/IM8442
  • https://www.mathnet.ru/eng/im/v81/i3/p83
  • This publication is cited in the following 11 articles:
    1. A. Yu. Trynin, “Ob odnom metode resheniya smeshannoi kraevoi zadachi dlya uravneniya parabolicheskogo tipa s pomoschyu operatorov ATλ,j”, Izv. vuzov. Matem., 2024, no. 2, 59–80  mathnet  crossref
    2. A. Yu. Trynin, “On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators ATλ,j”, Russ Math., 68:2 (2024), 52  crossref
    3. A. Yu. Trynin, “A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators ATλ,j”, Izv. Math., 87:6 (2023), 1227–1254  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. A. Yu. Trynin, “On a method for solving a mixed boundary value problem for a parabolic equation using modified sinc-approximation operators”, Comput. Math. Math. Phys., 63:7 (2023), 1264–1284  mathnet  mathnet  crossref  crossref  mathscinet
    5. Pavel Shabalin, Rafael Faizov, E. Vdovin, “Hilbert boundary value problem for generalized analytic functions with a singular line”, E3S Web Conf., 274 (2021), 11003  crossref  mathscinet
    6. A. H. Babayan, Springer Proceedings in Mathematics & Statistics, 357, Operator Theory and Harmonic Analysis, 2021, 55  crossref
    7. N. A. Zhura, A. P. Soldatov, “Problem of the Riemann-Hilbert type for a hyperbolic system on the plane”, Differ. Equ., 55:6 (2019), 815–823  crossref  mathscinet  zmath  isi  scopus
    8. Armenak H. Babayan, Seyran H. Abelyan, Springer Proceedings in Mathematics & Statistics, 291, Modern Methods in Operator Theory and Harmonic Analysis, 2019, 317  crossref
    9. V. P. Radchenko, A. A. Andreev, E. A. Kozlova, “K 70-letiyu professora Aleksandra Pavlovicha Soldatova”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:1 (2018), 15–22  mathnet  crossref  zmath  isi  elib
    10. A. P. Soldatov, “Characteristically Closed Domains for First Order Strictly Hyperbolic Systems in the Plane”, J Math Sci, 232:4 (2018), 552  crossref  mathscinet
    11. N. A. Zhura, V. A. Polunin, “Dirichlet type problem for strictly hyperbolic systems of first order with constant coefficients in two dimensional domain”, J. Math. Sci., 237:4 (2019), 595–609  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:490
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    References:71
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