Hyberbolic Conservation Laws in Continuum Physics
This masterly exposition of the mathematical theory of hyperbolic system for conservation laws brings out the intimate connection with continuum thermodynamics, by emphasising issues in which the analysis may reveal something about the physics and, in ret
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Series editors M. Berger B. Eckmann P. de la Harpe F. Hirzebruch N. Hitchin L. Hörmander M.-A. Knus A. Kupiainen G. Lebeau M. Ratner D. Serre Ya. G. Sinai N. J. A. Sloane B. Totaro A. Vershik M. Waldschmidt
Editors-in-Chief A. Chenciner
J. Coates
S. R. S. Varadhan
Constantine M. Dafermos
Hyberbolic Conservation Laws in Continuum Physics Second Edition With 38 Figures
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Constantine M. Dafermos Division of Applied Mathematics Brown University Providence, RI 02912 USA e-mail: [email protected]
Library of Congress Control Number: 2005929877
Mathematics Subject Classification (2000): 35L65, 35L67, 73Bxx, 76L05
ISSN 0072-7830 ISBN-10 3-540-25452-8 Springer Berlin Heidelberg New York ISBN-13 978-3-540-25452-2 Springer Berlin Heidelberg New York ISBN 3-540-64914-X 1st ed. Springer-Verlag Berlin Heidelberg New York 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 permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 1999, 2005 Printed in Germany 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: design & production GmbH, Heidelberg Printed on acid-free paper
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For Mihalis and Thalia
Preface to the Second Edition
It is a testament to the vitality of the field of conservation laws that five years after the original publication of this work it has become necessary to prepare a considerably revised and expanded second edition. A new chapter has been added, recounting the exciting recent developments on the vanishing viscosity method; and numerous new sections have been incorporated in preexisting chapters, to introduce newly derived results or present older material, omitted in the first edition, whose relevance and importance has been underscored by current trends in research. This includes recent work by the author, which has not been published elsewhere. In addition, a substantial portion of the original text has been revamped so as to streamline the exposition, enrich the collection of examples, and improve the notation. The introduction has been revised to reflect these changes. The bibliography has been updated and expanded as well, now comprising over one thousand titles. Twenty-five years ago, it might have been feasible to compose a treatise surveying the entire area; howe
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