International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 24, Pages 1279-1291
doi:10.1155/S0161171204204240
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.