Nonlocal problem with dynamical boundary conditions for hyperbolic equation

In this article, we consider a boundary-value problem with nonlocal dynamical conditions for hyperbolic equation. A feature of such conditions is the presence of both first and second order derivatives with respect to time-variable. Furthermore, boundary conditions are nonlocal to the extent that their representation is a relation between values of the derivatives on different parts of the boundary. The problem under consideration arise when we study vibration of a bar with damping and point masses. The existence and uniqueness of a generalized solution are proved. The proof is based on apriori estimates and Galerkin procedure.