Kinetic Formulation of Conservation Laws (Oxford Lecture Series in Mathematics and Its Applications) - Hardcover

Perthame, B.; Perthame, Benoit

 
9780198509134: Kinetic Formulation of Conservation Laws (Oxford Lecture Series in Mathematics and Its Applications)
Hardcover
ISBN 10: 0198509138 ISBN 13: 9780198509134
Verlag: Oxford University Press, 2003

Inhaltsangabe

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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Über die Autorin bzw. den Autor

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

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Verlag
Oxford University Press
Erscheinungsdatum
2003
Sprache
Englisch
ISBN 10 
0198509138
ISBN 13 
9780198509134
Einband
Gebundene Ausgabe
Anzahl der Seiten
212
Kontakt zum Hersteller
preigu GmbH & Co. KG
mail@preigu.de

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