Dirichlet Problem for a Two-Dimensional Wave Equationin a Cylindrical Domain

The first boundary value problem is studied for a two-dimensional wave equation in a cylindrical domain. A uniqueness criterion is established. The solution is constructed as the sum of an orthogonal series. When justifying the convergence of the series, the problem of small denominators from two positive integer arguments is solved. An estimate for separation from zero with the corresponding asymptotics is established, which permits proving the convergence of the series in the class of regular solutions and the stability of the solution.