Stability and forward attractors for non-autonomous impulsive semidynamical systems

Everaldo de Mello Bonotto; Daniela Paula Demuner

doi:10.3934/cpaa.2020087

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2020, Volume 19, Issue 4: 1979-1996. Doi: 10.3934/cpaa.2020087

This issue Previous Article Controllability of the one-dimensional fractional heat equation under positivity constraints Next Article Forwards dynamics of non-autonomous dynamical systems: Driving semigroups without backwards uniqueness and structure of the attractor

Stability and forward attractors for non-autonomous impulsive semidynamical systems

Everaldo de Mello Bonotto^1, , and
Daniela Paula Demuner^2,

1.
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970, São Carlos SP, Brazil
2.
Universidade Federal do Espírito Santo, Vitória ES, Brazil

^* Corresponding author.
^* Corresponding author.

Dedicated to Tomás Caraballo on his 60th birthday

Received: March 31, 2019

Revised: September 30, 2019

Published: January 2020

The first author is supported partially by FAPESP grant 2016/24711-1 and CNPq grant 310497/2016-7

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Abstract

In this paper, we study the theory of forward attractors for non-autonomous impulsive semidynamical systems. Moreover, we investigate some types of stability of the global attractor as orbital stability, asymptotic stability and stability in the sense of Lyapunov-Barbashin. We present an example to illustrate the theory.

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Mathematics Subject Classification: Primary: 34D20, 34D45; Secondary: 34A37.

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