The Dirichlet problem for telegraph equation in a rectangular domain

We investigate the Dirichlet problem for the telegraph equation in a rectangular domain. We establish a criterion of uniqueness of solution to the problem. The solution is constructed as the sum of an orthogonal series. In substantiation of convergence of the series, the problem of small denominators occurs. In connection with this, we establish estimates ensuring separation from zero of denominators with the corresponding asymptotics which allow us to prove the existence of a regular solution and prove its stability under small perturbations of boundary functions. © 2017, Allerton Press, Inc.