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July  2009, 23(3): 1041-1060. doi: 10.3934/dcds.2009.23.1041

A discretization scheme for an one-dimensional reaction-diffusion equation with delay and its dynamics

Maria do Carmo Pacheco de Toledo 1, and  Sergio Muniz Oliva 2,

1. 

Departamento de Ciências Exatas, Universidade Federal de Lavras, Lavras, MG, Brazil
2. 

Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, SP, Brazil

Received  December 2007 Revised  September 2008 Published  November 2008

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution $u$, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.
Keywords: reaction-diffusion equation with delay, discretization, asymptotic dynamic behavior.
Mathematics Subject Classification: Primary: 35K57,35M99,35R10; Secondary: 35B40,37L25.
Citation: Maria do Carmo Pacheco de Toledo, Sergio Muniz Oliva. A discretization scheme for an one-dimensional reaction-diffusion equation with delay and its dynamics. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 1041-1060. doi: 10.3934/dcds.2009.23.1041
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