Generalized Kinetic Models in Applied Sciences: Lecture Notes on Mathematical Problem

by Arlotti, Luisa; Bellomo, Nicola; De Angelis, Elena; Lachowicz, Miroslaw; Arlotti, Luisa

• ISBN13: 9789812385604
• ISBN10: 9812385606
• Format: Hardcover
• Copyright: 2003-11-01
• Publisher: World Scientific Pub Co Inc

Summary

This book deals with analytic problems related to some developments and generalizations of the Boltzmann equation toward the modeling and qualitative analysis of large systems that are of interest in applied sciences. These generalizations are documented in the various surveys edited by Bellomo and Pulvirenti with reference to models of granular media, traffic flow, mathematical biology, communication networks, and coagulation models. The first generalization dealt with refers to the averaged Boltzmann equation, which is obtained by suitable averaging of the distribution function of the field particles into the action domain of the test particle. This model is further developed to describe equations with dissipative collisions and a class of models that are of interest in mathematical biology. In this latter case the state of the particles is defined not only by a mechanical variable but also by a biological microscopic state.

Table of Contents

Preface
From the Boltzmann Equation to the Averaged Boltzmann Equation	p. 1
On the Cauchy Problem for the Averaged Boltzmann Equation	p. 37
Asymptotic Theory for the Averaged Boltzmann Equation	p. 79
Kinetic (Boltzmann) Models: Modeling and Analytic Problems	p. 141
Critical Analysis and Research Perspectives	p. 187
Collective Bibliography	p. 195
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