Attractors for impulsive non-autonomous dynamical systems and their relations

In this work, we deal with several different notions of attractors that may appear in the impulsive non-autonomous framework and we explore their relationships to obtain properties regarding the different scenarios of asymptotic dynamics, such as the cocycle attractor, the uniform attractor and the...

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Bibliographic Details
Published in:Journal of Differential Equations 2017-03, Vol.262 (6), p.3524-3550
Main Authors: Bonotto, E.M., Bortolan, M.C., Caraballo, T., Collegari, R.
Format: Article
Language:English
Subjects:
c-Global attractor
Cocycle attractor
Global attractor
Impulsive non-autonomous dynamical systems
Skew-product semiflow
Uniform attractor
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Summary:In this work, we deal with several different notions of attractors that may appear in the impulsive non-autonomous framework and we explore their relationships to obtain properties regarding the different scenarios of asymptotic dynamics, such as the cocycle attractor, the uniform attractor and the global attractor for the impulsive skew-product semiflow. Lastly, we illustrate our theory by exhibiting an example of a non-classical non-autonomous parabolic equation with subcritical nonlinearity and impulses.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2016.11.036