Abstract and Applied Analysis
Volume 2003 (2003), Issue 16, Pages 899-922
doi:10.1155/S1085337503305019
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.