Copyright © 2004 Hindawi Publishing Corporation. 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.

Abstract

We investigate an initial boundary value problem for a second-order hyperbolic equation with only integral conditions. We show the existence, uniqueness, and continuous dependence of a strongly generalized solution. The proof is based on an energy inequality established in a nonclassical function space, and on the density of the range of the operator associated to the abstract formulation of the studied problem by introducing special smoothing operators.