International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 4, Pages 201-213
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 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.
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.