Pullback exponential attractors for differential equations with delay

Sana Netchaoui; Mohamed Ali Hammami; Tomás Caraballo

doi:10.3934/dcdss.2020367

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2021, Volume 14, Issue 4: 1345-1358. Doi: 10.3934/dcdss.2020367

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Pullback exponential attractors for differential equations with delay

1.
Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Route de la Soukra km 4 Sfax 3038, Tunisia
2.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, c/ Tarfia s/n, 41012-Sevilla, Spain

Received: July 31, 2019

Revised: December 31, 2019

Early access: May 2020

Published: April 2021

This work has been partially supported by FEDER and the Spanish Ministerio de Ciencia, Innovación y Universidades under project PGC2018-096540-B-I00, and Proyecto I+D+i Programa Operativo FEDER Andalucía US-1254251

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Abstract

We show the existence of an exponential attractor for non-autono-mous dynamical system with bounded delay. We considered the case of strong dissipativity then prove that the result remains for the weak dissipativity. We conclude then the existence of the global attractor and ensure the boundedness of its fractal dimension.

Keywords:

non-autonomous delay differential equations,
variable delays,
distributed delay,
integro-differential equation,
pullback exponential attractors,
fractal dimension,
non-autonomous dynamical systems.

Mathematics Subject Classification: Primary 37B55; Secondary 34D45, 37L25.

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References

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