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Book synopsis

This work 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 above literature motivates applied mathematicians to study the Cauchy problem and to develop an asymptotic analysis for models regarded as developments of the Boltzmann equation. This book aims to initiate the research plan by the analyzing aforementioned analysis problems. 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. The book is essentially devoted to analytic aspects and deals with the analysis of the Cauchy problem and with the development of an asymptotic theory to obtain the macroscopic description from the mesoscopic one.

Book details

Book category Books in English Mathematics & science Science: general issues Maths for scientists

• Full title: Generalized Kinetic Models In Applied Sciences: Lecture Notes On Mathematical Problems
• Author: Miroslaw Lachowicz, Nicola Bellomo, Luisa Arlotti
• Language: English
• Binding: Hardback
• Number of pages: 220
• EAN: 9789812385604
• ISBN: 9812385606
• ID: 05067615
• Publisher: World Scientific Publishing Co Pte Ltd
• Weight: 18 g
• Date of publishing: 13. August 2003

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