International Journal of Stochastic Analysis
Volume 2010 (2010), Article ID 519684, 16 pages
doi:10.1155/2010/519684
Research Article

The Rothe's Method to a Parabolic Integrodifferential Equation with a Nonclassical Boundary Conditions

Abdelfatah Bouziani and Rachid Mechri

Department of Mathematics, University of Larbi Ben M'Hidi, Oum El Bouagui 04000, Algeria

Received 26 February 2009; Revised 17 August 2009; Accepted 10 December 2009

Academic Editor: Alexander M. Krasnosel'skii

Copyright © 2010 Abdelfatah Bouziani and Rachid Mechri. 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

This paper is devoted to prove, in a nonclassical function space, the weak solvability of parabolic integrodifferential equations with a nonclassical boundary conditions. The investigation is made by means of approximation by the Rothes method which is based on a semidiscretization of the given problem with respect to the time variable.