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