International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 24, Pages 1279-1291

A mixed problem with only integral boundary conditions for a hyperbolic equation

Abdelfatah Bouziani

Département de Mathématiques, Centre Universitaire Larbi Ben M'hidi, Oum El Bouagui 04000, Algeria

Received 29 April 2002

Copyright © 2004 Abdelfatah Bouziani. 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.


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.