Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 34053, 20 pages
doi:10.1155/JAMSA/2006/34053

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

Abstract

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.