Un approccio multiscala alla dinamica delle folle mediante misure che evolvono nel tempo

This paper deals with models of living complex systems, chiefly human crowds, by methods of conservation laws and measure theory. We introduce a modeling framework which enables one to address both discrete and continuous dynamical systems in a unified manner using common phenomenological ideas and mathematical tools as well as to couple these two descriptions in a multiscale perspective. Furthermore, we present a basic theory of well-posedness and numerical approximation of initial-value problems and we discuss its implications on mathematical modeling.