Copyright © 2010 Akbar B. Aliev and Ulviya M. Mamedova. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The initial-boundary value problem for a class of linear and nonlinear equations
in Hilbert space is considers. We prove the existence and uniqueness of solution of
this problem. The results of this investigation are applied to solvability of initial-boundary
value problems for quasilinear impulsive hyperbolic equations with non-stationary
transmission and boundary conditions.