Inverse Problems for Initial Conditions of the Mixed Problem for the Telegraph Equation

Abstract

In this paper, we examine inverse problems for initial conditions for the wave and telegraph equations and state uniqueness criteria. Solutions of these problems are constructed in the series form. In the proof of uniform convergence of these series, the problem on small denominators appears. We prove estimates of small denominators separated from zero and obtain asymptotics that allow one to justify the convergence in the class of regular solutions.