Overview
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.
Full Product Details
Author: Benoit Perthame (, Ecole Normale Superieure, Paris)
Publisher: Oxford University Press
Imprint: Oxford University Press
Dimensions:
Width: 16.10cm
, Height: 1.60cm
, Length: 24.20cm
Weight: 0.431kg
ISBN: 9780198509134
ISBN 10: 0198509138
Pages: 212
Publication Date: 05 December 2002
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: To order
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.
Reviews
"""Kinetic Formulation has received wide attention and Perthame is the person most responsible for it."" T-P Liu, Department of Mathematics, Stanford, CA ""A well-known expert, who made some of the key breakthroughs in this area."" A Bressan, SISSA, Trieste, Italy ""It has been known within the community that Benoit Perthame is writing such a book. The book is anticipated from the community and expected to fill a gap in the literature."" A Tzavaras, Department of Mathematics, University of Wisconsin-Madison"
The book is a good introduction into the theory of kinetic formulations of conservation laws written by the leading expert in the field. A list of open problems and the extensive bibliography also makes it a starting point for further research. Zentralblatt MATH
Author Information
Prof. Benoit Perthame ENS/DMA 45, rue d'Ulm; F-75230 Paris Cedex 05 FRANCE 33-1-44322036 phone 33-1-44322080 fax benoit.perthame@ens.fr French, born France, June 23 1959
