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

Abdelfatah Bouziani

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 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 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.