Abstract and Applied Analysis
Volume 2003 (2003), Issue 16, Pages 899-922
doi:10.1155/S1085337503305019
Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation
Nabil Merazga
and Abdelfatah Bouziani
Département de Mathématiques, Centre Universitaire Larbi Ben M'hidi, Oum El Bouagui 04000, Algeria
Abstract
This paper deals with an initial boundary value problem with an integral condition for the two-dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one-dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are proved by means of the Rothe method. Besides, convergence and an error estimate for a semidiscrete approximation are obtained.