Geodesic
A boundary-value problem for a~first-order hyperbolic system in a~two-dimensional domain
Izvestiya. Mathematics , Tome 81 (2017) no. 3, pp. 542-567

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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. 
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     author = {N. A. Zhura and A. P. Soldatov},
     title = {A boundary-value problem for a~first-order hyperbolic system in a~two-dimensional domain},
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N. A. Zhura; A. P. Soldatov. A boundary-value problem for a~first-order hyperbolic system in a~two-dimensional domain. Izvestiya. Mathematics , Tome 81 (2017) no. 3, pp. 542-567. http://geodesic.mathdoc.fr/item/IM2_2017_81_3_a3/