Convergences of asymptotically autonomous pullback attractors towards semigroup attractors

Hongyong Cui

doi:10.3934/dcdsb.2018276

Article Contents

2019, Volume 24, Issue 8: 3525-3535. Doi: 10.3934/dcdsb.2018276

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Convergences of asymptotically autonomous pullback attractors towards semigroup attractors

Hongyong Cui

School of Mathematics and Statistics, Huazhong University of Science & Technology, Wuhan 430074, China

Dedicated to Professor Peter Kloeden on his 70th birthday

Received: November 2017

Revised: May 2018

Early access: October 10, 2018

Published online: October 10, 2018

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Abstract

For pullback attractors of asymptotically autonomous dynamical systems we study the convergences of their components towards the global attractors of the limiting semigroups. We use some conditions of uniform boundedness of pullback attractors, instead of uniform compactness conditions used in the literature. Both forward convergence and backward convergence are studied.

Keywords:

Asymptotically autonomous dynamical system,
pullback attractor,
limiting equation,
upper semi-continuity.

Mathematics Subject Classification: Primary: 35B40; Secondary: 35B41, 37L30.

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