Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 2, Pages 117-128
An abstract inverse problem
Université de france-comté, Laboratory de Mathématiques, route de Gray, Besançon cédex 25030, France
Received 1 January 1990; Revised 1 October 1990
Copyright © 1991 M. Choulli. 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.
In this paper we consider an inverse problem that corresponds to an
abstract integrodifferential equation. First, we prove a local existence and
uniqueness theorem. We also show that every continuous solution can be
locally extended in a unique way. Finally, we give sufficient conditions for the
existence and a stability of the global solution.