International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 82654, 10 pages
doi:10.1155/IJMMS/2006/82654
Remarks on weak solutions for a nonlocal parabolic problem
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.
Abstract
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.