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

Maria do Carmo Pacheco de Toledo; Sergio Muniz Oliva

doi:10.3934/dcds.2009.23.1041

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2009, Volume 23, Issue 3: 1041-1060. Doi: 10.3934/dcds.2009.23.1041

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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
2.
Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, SP

Received: November 30, 2007

Revised: August 31, 2008

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K57,35M99,35R10; Secondary: 35B40,37L25.

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

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