Impulsive non-autonomous dynamical systems and impulsive cocycle attractors

Author(s)

Bonotto, Everaldo M. ; Bortolan, Matheus C. ; Caraballo, Tomas ; Collegari, Rodolfo

• Document type: Journal article
• Source: MATHEMATICAL METHODS IN THE APPLIED SCIENCES; v. 40, n. 4, p. 1095-1113, MAR 15 2017.
• Web of Science Citations: 5

Abstract

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 (C) 2016 JohnWiley \& Sons, Ltd. (AU)

• FAPESP's process: 14/25970-5 - Evolution processes with impulses and the attractor theory
• Grantee: Everaldo de Mello Bonotto
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 14/20691-0 - Pullback attractos in impulsive evolution process
• Grantee: Rodolfo Collegari
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 13/23933-2 - Pullback attractors in impulsive semidynamical systems
• Grantee: Rodolfo Collegari
• Support Opportunities: Scholarships in Brazil - Post-Doctoral