# American Institute of Mathematical Sciences

May  2020, 40(5): 2791-2826. doi: 10.3934/dcds.2020150

## Pullback attractors to impulsive evolution processes: Applications to differential equations and tube conditions

 1 Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis - Brazil 2 Departamento de Estatística, Análise Matemática e Optimización & Instituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela - Spain

* Corresponding author: Matheus C. Bortolan

Received  July 2019 Published  March 2020

Fund Project: The first author is by supported by CNPq, project # 407635/2016-5. The second author was partially supported by the predoctoral contact BES-2017-082334

We define the notions of impulsive evolution processes and their pullback attractors, and exhibit conditions under which a given impulsive evolution process has a pullback attractor. We apply our results to a nonautonomous ordinary differential equation describing an integrate-and-fire model of neuron membrane, as well as to a heat equation with nonautonomous impulse and a nonautonomous 2D Navier-Stokes equation. Finally, we introduce the notion of tube conditions to impulsive evolution processes, and use them as an alternative way to obtain pullback attractors.

Citation: Matheus C. Bortolan, José Manuel Uzal. Pullback attractors to impulsive evolution processes: Applications to differential equations and tube conditions. Discrete & Continuous Dynamical Systems - A, 2020, 40 (5) : 2791-2826. doi: 10.3934/dcds.2020150
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