Attractors for impulsive non-autonomous dynamical systems and their relations

Author(s)

Bonotto, E. M. ^[1] ; Bortolan, M. C. ; Caraballo, T. ; Collegari, R. ^[4]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Campus Sao Carlos, Caixa Postal 668, Sao Carlos, SP, Brazil. Bortolan, M. C., Univ Fed Santa Catarina, Dept Matemat, Campus Trindade, BR-88040900 Florianopolis, SC, Brazil. Caraballo, T., Univ Seville, Dept Ec - Spain

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Campus Sao Carlos, Caixa Postal 668, Sao Carlos, SP, Brazil. Bortolan, M. C., Univ Fed Santa Catarina, Dept Matemat, Campus Trindade, BR-88040900 Florianopolis, SC, Brazil. Caraballo, T., Univ Seville, Dept Ecuac Diferenciales & Anal Numer EDAN, Seville - Spain

• Document type: Journal article
• Source: Journal of Differential Equations; v. 262, n. 6, p. 3524-3550, MAR 15 2017.
• Web of Science Citations: 7

Abstract

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. (C) 2016 Elsevier Inc. All rights reserved. (AU)

• 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: 14/25970-5 - Evolution processes with impulses and the attractor theory
• Grantee: Everaldo de Mello Bonotto
• Support Opportunities: Scholarships abroad - Research