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
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.