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

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.