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 d ynamics 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 qualitat ive analysis of the initial and initial boundary value problems. The third part of the paper provides a survey of applications and develops an analysi s of some open problems. (C) 1999 Elsevier Science Ltd. All rights reserved .