Modelling aggregation–fragmentation phenomena from kinetic to macroscopic scales

This paper deals with the modelling of aggregation and/or fragmentation physical phenomena for large systems of interacting living entities in the framework of the mathematical kinetic theory for active particles. After introducing various mathematical structures in terms of systems of nonlinear integro-differential equations with quadratic type nonlinearities and variable number of equations, the relative qualitative analysis of the initial value problem is presented. Finally, the paper deals with the derivation of macroscopic equations based on the underlying description at the microscopic scale delivered by the kinetic theory models.