The Dirichlet Problem for a Hyperboli-Type Equation with Power Degeneracy in a Rectangular Domain

Abstract

The first boundary value problem is studied for a linear hyperbolic equation in a rectangle with a power degeneracy on one of its sides for different degrees of degeneracy. A uniqueness criterion is established. The solution is constructed as the sum of a Fourier series. The problem of small denominators arises when justifying the convergence of this series. In this connection, some estimates for the separation of the small denominators from zero are established with the corresponding asymptotics specified. It is these asymptotics that have made it possible to substantiate the existence of a regular problem solution.