Overview

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.

Full Product Details

Author:   Fraydoun Rezakhanlou ,  François Golse ,  Cédric Villani ,  Stefano Olla
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2008 ed.
Volume:   1916
Dimensions:   Width: 15.50cm , Height: 0.80cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783540737049

ISBN 10:   3540737049
Pages:   113
Publication Date:   14 November 2007
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Reviews

From the reviews: This nice book is based on two courses given, respectively, by Fraydoun Rezakhanlou and Cedric Villani at the Centre Aemile Borel of the Institut Henri Poincare 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. (Clement Mouhot, Mathematical Reviews, Issue 2010 h)

From the reviews: This nice book is based on two courses given, respectively, by Fraydoun Rezakhanlou and Cedric Villani at the Centre Emile Borel of the Institut Henri Poincare 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. (Clement Mouhot, Mathematical Reviews, Issue 2010 h)

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