PULLBACK ATTRACTORS TO IMPULSIVE EVOLUTION PROCESSES: APPLICATIONS TO DIFFERENTIAL EQUATIONS AND TUBE CONDITIONS

摘要

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 nonautono-mous 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.