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Impulsive non‐autonomous dynamical systems and impulsive cocycle attractors
Author(s) -
Bonotto Everaldo M.,
Bortolan Matheus C.,
Caraballo Tomás,
Collegari Rodolfo
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4038
Subject(s) - attractor , mathematics , dynamical systems theory , autonomous system (mathematics) , dynamical system (definition) , work (physics) , control theory (sociology) , mathematical analysis , computer science , control (management) , artificial intelligence , physics , quantum mechanics , thermodynamics
In this work, we define the notions of ‘impulsive non‐autonomous dynamical systems’ and ‘impulsive cocycle attractors’. Such notions generalize (we will see that not in the most direct way) the notions of autonomous dynamical systems and impulsive global attractors in the current published literature. We also establish conditions to ensure the existence of an impulsive cocycle attractor for a given impulsive non‐autonomous dynamical system, which are analogous to the continuous case. Moreover, we prove the existence of such attractor for a non‐autonomous 2D Navier–Stokes equation with impulses, using energy estimates. Copyright © 2016 John Wiley & Sons, Ltd.