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Entropy Methods for the Boltzmann Equation

Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001

  • Book
  • © 2008

Overview

Authors:
  1. Fraydoun Rezakhanlou

    1. Department of Mathematics Evans Hall, University of California, Berkeley, USA

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  2. Cédric Villani

    1. Unité de mathématiques pures et appliquées (UMR CNRS 5669), Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France

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Editors:
  1. François Golse

    1. Laboratoire Jacques-Louis Lions (UMR CNRS 7598), Université Pierre et Marie Curie, Paris, France

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  2. Stefano Olla

    1. Centre de recherche en mathématiques de la décision (UMR CNRS 7534), Université Paris - Dauphine, Paris Cedex 16, France

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1916)

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Table of contents (2 chapters)

  1. Front Matter

    Pages i-xii
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  2. Entropy Production and Convergence to Equilibrium

    • C. Villani
    Pages 1-70

  3. Kinetic Limits for Interacting Particle Systems

    • F. Rezakhanlou
    Pages 71-105

  4. Back Matter

    Pages 107-111
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Keywords

About this book

Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level.

During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.

Reviews

From the reviews: “This nice book is based on two courses given, respectively, by Fraydoun Rezakhanlou and Cédric Villani at the Centre Émile Borel of the Institut Henri Poincaré in a special semester organized in the fall term of 2001 by Francois Golse and Stefano Olla. … discusses many extensions, open questions and perspectives which should be valuable for many researchers in the field of the Boltzmann equation. … This book … will be useful to all mathematicians interested in entropy methods.” (Clément Mouhot, Mathematical Reviews, Issue 2010 h)

Authors, Editors and Affiliations

  • Laboratoire Jacques-Louis Lions (UMR CNRS 7598), Université Pierre et Marie Curie, Paris, France

    François Golse

  • Centre de recherche en mathématiques de la décision (UMR CNRS 7534), Université Paris - Dauphine, Paris Cedex 16, France

    Stefano Olla

  • Department of Mathematics Evans Hall, University of California, Berkeley, USA

    Fraydoun Rezakhanlou

  • Unité de mathématiques pures et appliquées (UMR CNRS 5669), Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France

    Cédric Villani

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