Delio Mugnolo: Nonlinear difference operators on graphs

I will present an invitation to the theory of linear difference operators on graphs and discuss a few motivations for the introduction of some specific nonlinear generalizations. I will further perform a preliminary analysis of the associated time-continuous dynamical system, deducing its well-posedness and some qualitative properties of its solutions. In particular, I will try to shed light on the interplay between some analytic properties of the solution of said dynamical system and the features of the underlying graph.