Lecture notes on the mathematical theory of generalized Boltzmann models (Q2734831)

This book deals with the derivation, analysis and application of generalized kinetic models, and it describes how theory may be various fields of applied sciences: astrophysics, traffic flow, mathematical biology, theoretical immunology, social science etc. The literature on these models, that are characterized by a mathematical structure somewhat similar to the nonlinear Boltmann equation, is generally dispersed in several specialized areas. In this book the authors give a unified presentation of the whole, large and highly general class of models among which the Boltzmann equation can be regarded as a particular, however relevant, example. A generalized Boltzmann model consists in an evolution equation for the statistical distribution function over the physical state of individuals in a large population. The distribution function and the related moments are supposed to describe and characterize the system under investigation. NEWLINENEWLINENEWLINEThe contents of the book is developed as to take into account, that generalized kinetic models may be useful tools in describing a large class of complex physical systems. Moreover, mathematical problems related to the analysis of these models are often an interesting and challenging task for applied mathematics.