Impulses in driving semigroups of nonautonomous dynamical systems: Application to cascade systems

Everaldo de Mello Bonotto; Matheus Cheque Bortolan; Rodolfo Collegari; José Manuel Uzal

doi:10.3934/dcdsb.2020306

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2021, Volume 26, Issue 9: 4645-4661. Doi: 10.3934/dcdsb.2020306

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Impulses in driving semigroups of nonautonomous dynamical systems: Application to cascade systems

1.
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos - SP, 13566-590, Brazil
2.
Departamento de Matemática, Centro de Ciências Físicas e Matemáticas, Universidade Federal de Santa Catarina, Florianópolis-SC, 88040-900, Brazil
3.
Faculdade de Matemática, Universidade Federal de Uberlândia, Uberlândia-MG, 38400-902, Brazil
4.
Departamento de Estatística, Análise Matemática e Optimización & Instituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

^* Corresponding author
^* Corresponding author

Received: March 31, 2020

Revised: July 31, 2020

Early access: October 2020

Published: September 2021

The first author is partially supported by FAPESP grant 2016/24711-1 and CNPq grant 310497/2016-7. The second author is partially supported by CNPq, project # 407635/2016-5. The third author is partially supported by FAPEMIG, project # APQ-00371-18.The fourth author is partially supported by the predoctoral contact BES-2017-082334

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Abstract

In this paper we investigate the long time behavior of a nonautonomous dynamical system (cocycle) when its driving semigroup is subjected to impulses. We provide conditions to ensure the existence of global attractors for the associated impulsive skew-product semigroups, uniform attractors for the coupled impulsive cocycle and pullback attractors for the associated evolution processes. Finally, we illustrate the theory with an application to cascade systems.

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Mathematics Subject Classification: Primary:35B41;Secondary:34A37, 35R12.

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References

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