Hyperbolic Conservation Laws in Continuum Physics
This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theor
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Series editors M. Berger P. de la Harpe F. Hirzebruch N. J. Hitchin L. Hörmander A. Kupiainen G. Lebeau M. Ratner D. Serre Ya. G. Sinai N.J.A. Sloane A. M. Vershik M. Waldschmidt Editor-in-Chief A. Chenciner J. Coates S.R.S. Varadhan
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For further volumes: http://www.springer.com/series/138
Constantine M. Dafermos
Hyperbolic Conservation Laws in Continuum Physics Third Edition
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Constantine M. Dafermos Division of Applied Mathematics CBrown University Providence, RI 02912 USA [email protected]
ISSN 0072-7830 ISBN 978-3-642-04047-4 e-ISBN 978-3-642-04048-1 DOI 10.1007/978-3-642-04048-1 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009934480 Mathematical Classification MSCs: 35L65, 35L67, 74-01, 76L05 © Springer-Verlag Berlin Heidelberg 1999, 2005, 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permissions for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
For Mihalis and Thalia
Preface to the Third Edition
The aim of this work is to present a broad overview of the theory of hyperbolic conservation laws, with emphasis on its genetic relation to classical continuum physics. It was originally published a decade ago, and a second, revised edition appeared in 2005. It is a testament to the vitality of the field that in order to keep up with recent developments it has become necessary to prepare a substantially expanded and updated new edition. A new chapter has been added, recounting the exciting recent developments in classical open problems in compressible fluid flow. Still another addition is an account of the early history of the subject, which had an interesting, tumultuous childhood. Furthermore, a substantial portion of the original text has been reorganized so as to streamline the exposition, update the information, and enrich the collection of examples. In particular, Chapter V has been completely revised. The bibliography has been updated and expanded as well, now comprising over fifteen hundred titles. The background, scope, and plan of the book are outlined in the Introduction, following this preface. Geometric measure theory, functional analysis and dynamical systems provide the necessary
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