A mixed problem with an integral condition for a hyperbolic equation. (Q1889551)

The paper is devoted to the study of a mixed problem for a second order hyperbolic equation with Neumann and nonlocal integral boundary conditions. These kind of integral conditions occur in the study of physical processes when data on the boundary are incompletely known as for instance in heat propagation, diffusion of particles in turbulent plasma, soil water transfer in capillary-porous media etc. For the stated problem one proves -- under certain circumstances -- the existence and uniqueness of a generalized solution. The existence is proved by using the Galerkin method and the proof of the uniqueness is based on a priori estimate in a function space introduced in the paper.