Kinetic Formulation of Conservation Laws by Benoit Perthame
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Kinetic Formulation of Conservation Laws
By Benoit Perthame

Kinetic Formulation of Conservation Laws

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Format: Hardback

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Kinetic Formulation of Conservation Laws by Benoit Perthame

Book Description

This book gives a general presentation of the mathematical and numerical connections kinetic theory and conservation laws based on several earlier works with P. L. Lions and E. Tadmor, as well as on more recent developments. The kinetic formalism approach allows the reader to consider Partial Differential Equations, such as some nonlinear conservation laws, as linear kinetic (or semi-kinetic) equations acting on a nonlinear quantity. It also aids the reader with using Fourier transform, regularisation, and moments methods to provide new approaches for proving uniqueness, regularizing effects, and a priori bounds. Special care has been given to introduce basic tools, including the classical Boltzmann formalism to derive compressible fluid dynamics, the study of oscillatons through the kinetic defect measure, and an elementary construction of solutions to scalar conservation laws. More advanced material contains regularizing effects through averaging lemmas, existence of global large solutions to isentropic gas dynamics, and a new uniqueness proof for scalar conservation laws. Sections are also devoted to the derivation of numerical approaches, the 'kinetic schemes', and the analysis of their theoretical properties.

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Book Details

ISBN: 9780198509134
ISBN-10: 0198509138
Format: Hardback
(242mm x 161mm x 16mm)
Pages: 212
Imprint: Clarendon Press
Publisher: Oxford University Press
Publish Date: 5-Dec-2002
Country of Publication: United Kingdom


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Author Biography - Benoit Perthame

Prof. Benoit Perthame ENS/DMA 45, rue d'Ulm; F-75230 Paris Cedex 05 FRANCE 33-1-44322036 phone 33-1-44322080 fax French, born France, June 23 1959

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