International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 24, Pages 1279-1291
doi:10.1155/S0161171204204240
A mixed problem with only integral boundary conditions for a
hyperbolic equation
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.
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.