Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 34053, 20 pages

Rothe time-discretization method for the semilinear heat equation subject to a nonlocal boundary condition

Nabil Merazga and Abdelfatah Bouziani

Département de Mathématiques, Centre Universitaire Larbi Ben M'hidi, Oum El Bouagui 04000, Algeria

Received 24 February 2006; Revised 28 May 2006; Accepted 29 May 2006

Copyright © 2006 Nabil Merazga and 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.


This paper is devoted to prove, in a nonclassical function space, the weak solvability of a mixed problem which combines a Neumann condition and an integral boundary condition for the semilinear one-dimensional heat equation. The investigation is made by means of approximation by the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable.