In a domain obtained as the Cartesian product of a segment by a circle of unit radius, we investigate a boundary-value problem with Dirichlet–Neumann conditions with respect to the time variable for a system of high-order hyperbolic equations with constant coefficients. We establish the conditions of unique solvability of the problem in the Sobolev spaces and construct its solution in the form of a vector series in a system of orthogonal functions. To establish lower estimates of small denominators encountered in the construction of solutions of the problem, we use the metric approach.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 57, No. 2, pp. 25–31, April–June, 2014.
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Ptashnyk, B.Y., Repetylo, S.M. Dirichlet–Neumann Problem for Systems of Hyperbolic Equations with Constant Coefficients. J Math Sci 215, 26–35 (2016). https://doi.org/10.1007/s10958-016-2819-9
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DOI: https://doi.org/10.1007/s10958-016-2819-9