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Author: Laure Saint-Raymond Publisher: Springer Science & Business Media ISBN: 3540928464 Category : Mathematics Languages : en Pages : 203
Book Description
"The material published in this volume comes essentially from a course given at the Conference on "Boltzmann equation and fluidodynamic limits", held in Trieste in June 2006." -- preface.
Author: Laure Saint-Raymond Publisher: Springer Science & Business Media ISBN: 3540928464 Category : Mathematics Languages : en Pages : 203
Book Description
"The material published in this volume comes essentially from a course given at the Conference on "Boltzmann equation and fluidodynamic limits", held in Trieste in June 2006." -- preface.
Author: Laure Saint-Raymond Publisher: Springer ISBN: 3540928472 Category : Science Languages : en Pages : 203
Book Description
The aim of this book is to present some mathematical results describing the transition from kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to hydrodynamics. Different fluid asymptotics will be investigated, starting always from solutions of the Boltzmann equation which are only assumed to satisfy the estimates coming from physics, namely some bounds on mass, energy and entropy.
Author: Alexander V. Bobylev Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110550172 Category : Mathematics Languages : en Pages : 275
Book Description
The series is devoted to the publication of high-level monographs and specialized graduate texts which cover the whole spectrum of applied mathematics, including its numerical aspects. The focus of the series is on the interplay between mathematical and numerical analysis, and also on its applications to mathematical models in the physical and life sciences. The aim of the series is to be an active forum for the dissemination of up-to-date information in the form of authoritative works that will serve the applied mathematics community as the basis for further research. Editorial Board Rémi Abgrall, Universität Zürich, Switzerland José Antonio Carrillo de la Plata, University of Oxford, UK Jean-Michel Coron, Université Pierre et Marie Curie, Paris, France Athanassios S. Fokas, Cambridge University, UK Irene Fonseca, Carnegie Mellon University, Pittsburgh, USA
Author: E.G.D. Cohen Publisher: Springer Science & Business Media ISBN: 3709183367 Category : Science Languages : en Pages : 647
Book Description
In,1872, Boltzmann published a paper which for the first time provided a precise mathematical basis for a discussion of the approach to equilibrium. The paper dealt with the approach to equilibrium of a dilute gas and was based on an equation - the Boltzmann equation, as we call it now - for the velocity distribution function of such ~ gas. The Boltzmann equation still forms the basis of the kinetic theory of gases and has proved fruitful not only for the classical gases Boltzmann had in mind, but als- if properly generalized - for the electron gas in a solid and the excitation gas in a superfluid. Therefore it was felt by many of us that the Boltzmann equation was of sufficient interest, even today, to warrant a meeting, in which a review of its present status would be undertaken. Since Boltzmann had spent a good part of his life in Vienna, this city seemed to be a natural setting for such a meeting. The first day was devoted to historical lectures, since it was generally felt that apart from their general interest, they would furnish a good introduction to the subsequent scientific sessions. We are very much indebted to Dr. D.
Author: Carlo Cercignani Publisher: Springer Science & Business Media ISBN: 1441985247 Category : Science Languages : en Pages : 357
Book Description
The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers. The project was in some sense inherited from our friend Marvin Shinbrot, who had planned a book about recent progress for the Boltzmann equation, but, due to his untimely death in 1987, never got to do it. When we drew up the first outline, we could not anticipate how long the actual writing would stretch out. Our ambitions were high: We wanted to cover the modern mathematical theory of the Boltzmann equation, with rigorous proofs, in a complete and readable volume. As the years progressed, we withdrew to some degree from this first ambition- there was just too much material, too scattered, sometimes incomplete, sometimes not rigor ous enough. However, in the writing process itself, the need for the book became ever more apparent. The last twenty years have seen an amazing number of significant results in the field, many of them published in incom plete form, sometimes in obscure places, and sometimes without technical details. We made it our objective to collect these results, classify them, and present them as best we could. The choice of topics remains, of course, subjective.
Author: C.M. Dafermos Publisher: Elsevier ISBN: 0080931979 Category : Mathematics Languages : en Pages : 609
Book Description
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Author: Alexander Sinitsyn Publisher: Elsevier ISBN: 0123877806 Category : Mathematics Languages : en Pages : 321
Book Description
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory.This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance. - Reviews the whole field from the beginning to today - Includes practical applications - Provides classical and modern (semi-analytical) solutions
Author: Yoshio Sone Publisher: Springer Science & Business Media ISBN: 146120061X Category : Science Languages : en Pages : 358
Book Description
This monograph is intended to provide a comprehensive description of the rela tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented. In addition, various interesting physical phenomena derived from the asymptotic theory are explained. The background of the asymptotic studies is explained in Chapter 1, accord ing to which the fluid-dynamic-type equations that describe the behavior of a gas in the continuum limit are to be studied carefully. Their detailed studies depending on physical situations are treated in the following chapters. What is striking is that the classical gas dynamic system is incomplete to describe the behavior of a gas in the continuum limit (or in the limit that the mean free path of the gas molecules vanishes). Thanks to the asymptotic theory, problems for a slightly rarefied gas can be treated with the same ease as the corresponding classical fluid-dynamic problems. In a rarefied gas, a temperature field is di rectly related to a gas flow, and there are various interesting phenomena which cannot be found in a gas in the continuum limit.
Author: Giovanni Naldi Publisher: Springer Science & Business Media ISBN: 0817649468 Category : Mathematics Languages : en Pages : 437
Book Description
Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.
Author: Laure Saint-Raymond
Author: Laure Saint-Raymond
Author: Laure Saint-Raymond
Author: Alexander V. Bobylev
Author: 
Author: E.G.D. Cohen
Author: Carlo Cercignani
Author: C.M. Dafermos
Author: Alexander Sinitsyn
Author: Yoshio Sone
Author: Giovanni Naldi