Mohamed Ali Hammami a, , Lassaad Mchiri a,b, , Sana Netchaoui a, and Stefanie Sonner c,,
Department of Mathematics, University of Sfax, Route de la Soukra km 4, Sfax 3038, Tunisia
Department of Statistics and Operations Research, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
IMAPP Mathematics, Radboud Universiteit Nijmegen, PO Box 9010, 6500GL Nijmegen, The Netherlands
* Corresponding author: Stefanie Sonner
Received February 2019 Published July 2019
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.
Citation: Mohamed Ali Hammami, Lassaad Mchiri, Sana Netchaoui, Stefanie Sonner. Pullback exponential attractors for differential equations with variable delays. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 301-319. doi: 10.3934/dcdsb.2019183
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Mohamed Ali Hammami Lassaad Mchiri Sana Netchaoui Stefanie Sonner