Bortolan, Matheus C.Uzal Couselo, José Manuel2024-02-082024-02-082020Bortolan, M. C., & Uzal, J. M. (2020). Pullback attractors to impulsive evolution processes: Applications to differential equations and tube conditions. Discrete And Continuous Dynamical Systems, 40(5), 2791-2826. https://doi.org/10.3934/dcds.20201501553-523110.3934/dcds.2020150https://hdl.handle.net/20.500.14352/100604We 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.engjournal articlehttps://doi.org/10.3934/dcds.2020150https://www.aimsciences.org/article/doi/10.3934/dcds.2020150restricted accessImpulsive evolution processesPullback semi attractorsPullback attractorsIntegrate-and-fire modelTube conditionsMatemáticas (Matemáticas)12 Matemáticas