Overview
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.
Full Product Details
Author: Luisa Arlotti (Univ Di Udine, Italy) ,
Nicola Bellomo (Politechnico Di Torino, Italy) ,
Elena De Angelis (Politechnico Di Torino, Italy) ,
Miroslaw Lachowicz (Warsaw Univ, Poland)
Publisher: World Scientific Publishing Co Pte Ltd
Imprint: World Scientific Publishing Co Pte Ltd
Edition: illustrated edition
Volume: 64
ISBN: 9789812385604
ISBN 10: 9812385606
Pages: 220
Publication Date: 13 August 2003
Audience:
College/higher education
,
Professional and scholarly
,
Postgraduate, Research & Scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Out of stock
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.
Reviews
"""This book may be useful for advanced graduate students and for scientists who are interested in mathematical problems of statistical mechanics and work in related fields of physics, mathematics and mechanics."" Zentralblatt MATH ""This book is valuable both for mathematicians and researchers working in applied sciences. It presents analytical tools and provides a wide overview of possible applications. I can definitely recommend this monograph to everyone interested in the subject of kinetic models. It is a valuable source of new mathematical ideas and modeling methods."" Siam Review"
This book may be useful for advanced graduate students and for scientists who are interested in mathematical problems of statistical mechanics and work in related fields of physics, mathematics and mechanics. Zentralblatt MATH This book is valuable both for mathematicians and researchers working in applied sciences. It presents analytical tools and provides a wide overview of possible applications. I can definitely recommend this monograph to everyone interested in the subject of kinetic models. It is a valuable source of new mathematical ideas and modeling methods. Siam Review
