Generalized Kinetic Models in Applied Sciences: Lecture Notes on Mathematical Problem (Series on Advances in Mathematics for Applied Sciences) (Vol 64) [Hardcover]

Luisa Arlotti (Author), Nicola Bellomo (Author), Elena De Angelis (Author), Miroslaw Lachowicz (Author)

Book Description

ISBN-10: 9812385606 | ISBN-13: 978-9812385604 | Publication Date: November 2003

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.

Editorial Reviews

Review

... a valuable source of new mathematical ideas and modeling methods. -- Siam Review

...useful for advanced graduate students and for scientists who are interested in mathematical problems of statistical mechanics. -- Zentralblatt MATH

From the Publisher

Graduate students, PhD students, academics and researchers in mathematical modeling and mathematical physics.

Product Details

• Hardcover: 220 pages
• Publisher: World Scientific Pub Co Inc (November 2003)
• Language: English
• ISBN-10: 9812385606
• ISBN-13: 978-9812385604
• Product Dimensions: 9.1 x 6.2 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #5,109,315 in Books (See Top 100 in Books)