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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 3, Pages 83–108 (Mi izv8442)  

This article is cited in 2 scientific papers (total in 2 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"

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.أش4
This paper was written with the support of International Project (3492.GF4) of the Ministry of Education and Science of Kazakhstan Republic.


DOI: https://doi.org/10.4213/im8442

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English version:
Izvestiya: Mathematics, 2017, 81:3, 542–567

Bibliographic databases:

UDC: 517.9
MSC: 35F45, 39B42, 47A10, 47B33
Received: 09.09.2015
Revised: 04.05.2016

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. A. Zhura, V. A. Polunin, “Zadachi tipa Dirikhle dlya strogo giperbolicheskikh sistem pervogo poryadka s postoyannymi koeffitsientami v dvumernoi oblasti”, Sib. zhurn. chist. i prikl. matem., 17:3 (2017), 17–32  mathnet  crossref
    2. 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
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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