Journal of Applied Mathematics
Volume 2003 (2003), Issue 10, Pages 487-502
doi:10.1155/S1110757X03204034
On initial boundary value problem with Dirichlet integral
conditions for a hyperbolic equation with the Bessel
operator
Department of Mathematics, The Larbi Ben M'hidi University Centre, P.O. Box. 565, Oum El Bouagui 04000, Algeria
Received 12 April 2002; Revised 15 June 2003
Copyright © 2003 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 consider a mixed problem with Dirichlet and integral
conditions for a second-order hyperbolic equation with the Bessel
operator. The existence, uniqueness, and continuous dependence of
a strongly generalized solution are proved. The proof is based on
an a priori estimate established in weighted Sobolev spaces and
on the density of the range of the operator corresponding to the
abstract formulation of the considered problem.