DIRICHLET PROBLEM FOR A TWO-DIMENSIONAL WAVE EQUATION IN A CYLINDRICAL DOMAIN

In this work, the first boundary value problem is studied for a two-dimensional wave equation in a cylindrical domain. A uniqueness criterion has been established. The solution is constructed as the sum of an orthogonal series. When justifying the convergence of a series, the problem of small denominators from two natural arguments arose for the first time. An estimate for separation from zero with the corresponding asymptotics was established, which made it possible to prove the convergence of the series in the class of regular solutions and the stability of the solution.