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.
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
\Bibitem{ZhuSol17}
\by N.~A.~Zhura, A.~P.~Soldatov
\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
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This publication is cited in the following 11 articles:
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
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
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
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
Pavel Shabalin, Rafael Faizov, E. Vdovin, “Hilbert boundary value problem for generalized analytic functions with a singular line”, E3S Web Conf., 274 (2021), 11003
A. H. Babayan, Springer Proceedings in Mathematics & Statistics, 357, Operator Theory and Harmonic Analysis, 2021, 55
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
Armenak H. Babayan, Seyran H. Abelyan, Springer Proceedings in Mathematics & Statistics, 291, Modern Methods in Operator Theory and Harmonic Analysis, 2019, 317
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
A. P. Soldatov, “Characteristically Closed Domains for First Order Strictly Hyperbolic Systems in the Plane”, J Math Sci, 232:4 (2018), 552
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