On an inverse boundary-value problem for the pseudohyperbolic equation with nonclassical boundary conditions

Abstract

In this paper, we consider an inverse boundary-value problem for a fourth-order pseudohyperbolic equation with nonclassical boundary conditions. The primary purpose of the work is to study the existence and uniqueness of the classical solution of the considered inverse boundary-value problem. To investigate the solvability of the considered problem, we carried out a transformation from the original problem to some auxiliary equivalent problem with trivial boundary conditions. Furthermore, we prove the existence and uniqueness theorem for the auxiliary problem by the contraction mappings principle. Based on the equivalency of these problems, the existence and uniqueness of the classical solution of the original problem are shown.