IMPULSIVE EVOLUTION PROCESSES: ABSTRACT RESULTS AND AN APPLICATION TO A COUPLED WAVE EQUATIONS

The aim of this paper is to study the long-time behavior of impulsive evolution processes. We obtain qualitative properties for impulsive evolution processes, and we prove an existence result of impulsive pullback attractors. Additionally, we provide sufficient conditions to obtain the upper semicontinuity at zero for a family of impulsive pullback attractors. As an application, we study the asymptotic dynamics of the following non-autonomous coupled wave system subject to impulsive effects at variable times, given by the following evolution system

Automated summary

The aim of this paper is to study the long-time behavior of impulsive evolution processes. We obtain qualitative properties for impulsive evolution processes, prove existence of impulsive pullback attractors, and provide conditions for the upper semicontinuity of a family of impulsive pullback attractors at zero. An application is made to study the asymptotic dynamics of a non-autonomous coupled wave system subject to impulsive effects at variable times.