About this Journal Submit a Manuscript Table of Contents
Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 679465, 30 pages
http://dx.doi.org/10.1155/2012/679465
Research Article

A Weak Comparison Principle for Reaction-Diffusion Systems

Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avenida Universidad s/n, 03202 Elche, Spain

Received 4 May 2012; Accepted 17 July 2012

Academic Editor: S. Romaguera

Copyright © 2012 José Valero. 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 weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L is proved for at least one solution of the problem.