Journal of Applied Mathematics
Volume 1 (2001), Issue 3, Pages 107-116
doi:10.1155/S1110757X01000365
Mixed problem with integral conditions for a certain class of hyperbolic equations
1Department of Mathematics, University of Tebessa, Tebessa 12002, Algeria
2Department of Mathematics, University of Oum El Bouaghi, BP 565, 04000, Algeria
Received 23 May 2001
Abstract
We study a mixed problem with purely integral conditions for a
class of two-dimensional second-order hyperbolic equations. We
prove the existence, uniqueness, and the continuous dependence
upon the data of a generalized solution. We use a functional
analysis method based on a priori estimate and on the density of
the range of the operator generated by the considered
problem.