Analysis and control of some evolutive models

The aim of this thesis is to investigate the asymptotic behavior of solutions to opinion formation and flocking models and to abstract evolution equations. Most of the models we will deal with involve time delay effects. Time delays, even arbitrarily small, may induce instability phenomena. Hence, the stability analysis for delayed systems is an important issue to deepen. In this thesis, we will establish consensus results for the Hegselmann-Krause opinion formation model and the Cucker-Smale flocking model, investigating different scenarios. Namely, we will analyze situations where lack of connections, non-universal interactions or repulsive dynamics may occur among the system's agents. Also, we will provide suitable decay estimates for solutions to linear evolution equations with time-dependent time delays and to semilinear evolution equations with memory and time-dependent time delay feedback.