Asymptotic behaviour of a logistic lattice system

Tomás Caraballo; Francisco Morillas; José Valero

doi:10.3934/dcds.2014.34.4019

Article Contents

2014, Volume 34, Issue 10: 4019-4037. Doi: 10.3934/dcds.2014.34.4019

This issue Previous Article Analysis and optimal control of some solidification processes Next Article The behavior of a beam fixed on small sets of one of its extremities

Asymptotic behaviour of a logistic lattice system

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla
2.
Department d'Economia Aplicada, Facultat d'Economia, Universitat de València, Campus del Tarongers s/n, 46022-València
3.
Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avda. de la Universidad, s/n, 03202 Elche

Received: November 30, 2012

Revised: January 31, 2013

Published: September 2014

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Abstract

In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we study a system of infinite ordinary differential equations which can be obtained after the spatial discretization of a logistic equation with diffusion. We prove that a global attractor exists in suitable weighted spaces of sequences.

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Mathematics Subject Classification: 35B40, 35B41, 35K55, 34G20, 37L30, 37L60.

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