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International Journal of Mathematics and Mathematical Sciences
Volume 31, Issue 4, Pages 201-213
http://dx.doi.org/10.1155/S0161171202005860

On the solvability of parabolic and hyperbolic problems with a boundary integral condition

1Département de Mathématiques, Centre Universitaire Larbi Ben M'hidi-Oum El Bouagui, B.P. 565, 04000, Algeria
2Mathematical Division, The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, Trieste 34100, Italy

Received 22 September 2000

Copyright © 2002 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 prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on the density of the range of the linear operator associated to the abstract formulation of the studied problem.