Pullback exponential attractors for differential equations with variable delays

Mohamed Ali Hammami; Lassaad Mchiri; Sana Netchaoui; Stefanie Sonner

doi:10.3934/dcdsb.2019183

Article Contents

2020, Volume 25, Issue 1: 301-319. Doi: 10.3934/dcdsb.2019183

This issue Previous Article Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay Next Article Error analysis of discontinuous Galerkin method for the time fractional KdV equation with weak singularity solution

Pullback exponential attractors for differential equations with variable delays

a.
Department of Mathematics, University of Sfax, Route de la Soukra km 4, Sfax 3038, Tunisia
b.
Department of Statistics and Operations Research, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
c.
IMAPP Mathematics, Radboud Universiteit Nijmegen, PO Box 9010, 6500GL Nijmegen, The Netherlands

^* Corresponding author: Stefanie Sonner
^* Corresponding author: Stefanie Sonner

Received: January 31, 2019

Early access: July 2019

Published: January 2020

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Abstract

We show how recent existence results for pullback exponential attractors can be applied to non-autonomous delay differential equations with time-varying delays. Moreover, we derive explicit estimates for the fractal dimension of the attractors.

As a special case, autonomous delay differential equations are also discussed, where our results improve previously obtained bounds for the fractal dimension of exponential attractors.

Keywords:

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

Mathematics Subject Classification: Primary: 37L30, 37B55; Secondary: 34D45, 37L25.

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References

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