Lecture Notes on the Mathematical Theory of the Boltzmann Equation PDF Download

Author: N. Bellomo
Publisher: World Scientific
ISBN: 9789810221669
Category : Science
Languages : en
Pages : 276

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Book Description
This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.

Author: V.V. Aristov
Publisher: Springer Science & Business Media
ISBN: 9401008663
Category : Science
Languages : en
Pages : 305

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Book Description
This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.

Author: Laure Saint-Raymond
Publisher: Springer Science & Business Media
ISBN: 3540928464
Category : Mathematics
Languages : en
Pages : 203

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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: N. Bellomo
Publisher: World Scientific
ISBN: 9812382259
Category : Science
Languages : en
Pages : 317

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Book Description
This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community.

Author:
Publisher: Springer Science & Business Media
ISBN: 3540737049
Category :
Languages : en
Pages : 122

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Book Description

Author: Stewart Harris
Publisher: Courier Corporation
ISBN: 0486143821
Category : Science
Languages : en
Pages : 242

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Book Description
This introductory graduate-level text emphasizes physical aspects of the theory of Boltzmann's equation in a detailed presentation that doubles as a practical resource for professionals. 1971 edition.

Author: Carlo Cercignani
Publisher: Birkhäuser
ISBN: 3034881657
Category : Science
Languages : en
Pages : 391

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Book Description
The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.

Author: S. Friedlander
Publisher: Gulf Professional Publishing
ISBN: 008053354X
Category : Science
Languages : en
Pages : 627

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Book Description
The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

Author: Ludwig Boltzmann
Publisher: Univ of California Press
ISBN: 0520327470
Category : Science
Languages : en
Pages : 500

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Book Description
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

Author: CŽdric Villani
Publisher: American Mathematical Soc.
ISBN: 0821844989
Category : Mathematics
Languages : en
Pages : 154

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Book Description
This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, taking the general form ${\frac{\partial f}{\partial t}}+ L f =0$. The question is whether and how one can overcome the degeneracy by exploiting commutators.