International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 82654, 10 pages

Remarks on weak solutions for a nonlocal parabolic problem

S. B. de Menezes

Departamento de Matemática, Universidade Federal do Pará, Belém 66075-110, Pará, Brazil

Received 7 May 2005; Revised 20 September 2005; Accepted 28 November 2005

Dedicated to Professor L. A. Medeiros on the occasion of his 80th birthday

Copyright © 2006 S. B. de Menezes. 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.


We prove a result on existence and uniqueness of weak solutions for a diffusion problem associated with nonlinear diffusions of nonlocal type studied by Chipot and Lovat (1999) by an application of the fixed point result of Schauder. Moreover, making use of Faedo-Galerkin approximation, coupled with some technical ideas, we establish a result on existence of periodic solution.