From the Jager and Segel model to kinetic population dynamics nonlinear evolution problems and applications

This paper deals with the analysis of a new class of models of population dynamics with competition and kinetic interactions. The content is organized in three parts. The first one refers to modelling in the framework of the so-called generalized Boltzmann models. The second part deals with qualitative analysis of the initial and initial boundary value problems. The third part of the paper provides a survey of applications and develops an analysis of some open problems.