On a problem for wave equation with local data on the whole boundary

Abstract

In the current paper we propose a new formulation of a local boundary value problem for a one-dimensional wave equation in a rectangular domain in which boundary conditions are given on the whole boundary. We prove the well-posedness of the boundary value problem in the classical and generalized senses. The proof of the well-posedness of the formulated problem is reduced to question of the existence and uniqueness of solutions of the corresponding functional equations.