Dirichlet–Neumann Problem for Systems of Hyperbolic Equations with Constant Coefficients

Abstract

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.