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

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  • Format: Hardcover
  • Copyright: 2003-11-01
  • Publisher: World Scientific Pub Co Inc
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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

From the Boltzmann Equation to the Averaged Boltzmann Equationp. 1
On the Cauchy Problem for the Averaged Boltzmann Equationp. 37
Asymptotic Theory for the Averaged Boltzmann Equationp. 79
Kinetic (Boltzmann) Models: Modeling and Analytic Problemsp. 141
Critical Analysis and Research Perspectivesp. 187
Collective Bibliographyp. 195
Table of Contents provided by Blackwell. All Rights Reserved.

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