Numerical and finite delay approximations of attractors for logistic differential-integral  equations with infinite delay

Tomás Caraballo; P.E. Kloeden; Pedro Marín-Rubio

doi:10.3934/dcds.2007.19.177

Article Contents

2007, Volume 19, Issue 1: 177-196. Doi: 10.3934/dcds.2007.19.177

This issue Previous Article Attractors for the viscous Camassa-Holm equation Next Article Global well-posedness of the Cauchy problem for nonlinear Schrödinger-type equations

Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
2.
FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.

Received: May 31, 2006

Revised: February 28, 2007

Published: December 2006

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Abstract

The upper semi-continuous convergence of approximate attractors for an infinite delay differential equation of logistic type is proved, first for the associated truncated delay equation with finite delay and then for a numerical scheme applied to the truncated equation.

Keywords:

Attractors for delay differential equations,
numerical and theoretical approximations of solutions.

Mathematics Subject Classification: Primary: 34D45, 34K28, 34K25, 34K07.

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Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay

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