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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Constantine M. Dafermos
Hyperbolic Conservation Laws in Continuum Physics Fourth Edition
Grundlehren der mathematischen Wissenschaften A Series of Comprehensive Studies in Mathematics Volume 325
Editors-in-Chief A. Chenciner J. Coates S.R.S. Varadhan Series editors M. Berger P. de la Harpe N.J. Hitchin A. Kupiainen G. Lebeau F.-H. Lin S. Mori B.C. Ngô M. Ratner D. Serre N.J.A. Sloane A.M. Vershik M. Waldschmidt
More information about this series at http://www.springer.com/series/138
Constantine M. Dafermos
Hyperbolic Conservation Laws in Continuum Physics Fourth Edition
123
Constantine M. Dafermos Providence, RI USA
ISSN 0072-7830 ISSN 2196-9701 (electronic) Grundlehren der mathematischen Wissenschaften ISBN 978-3-662-49449-3 ISBN 978-3-662-49451-6 (eBook) DOI 10.1007/978-3-662-49451-6 Library of Congress Control Number: 2016935976 © Springer-Verlag Berlin Heidelberg 1999, 2005, 2010, 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH Berlin Heidelberg
For Mihalis and Thalia
Preface to the Fourth Edition
The purpose 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. The background, scope and plan are outlined in the Introduction, following this preface. The book was originally published fifteen years ago, and a third, revised edition appeared in 2010. Nevertheless, in order to keep pace with recent developments in the area, it has become necessary to prepare this substantially expanded and updated new edition. In the face of the explosive growth of research, in volume, diversity and technical complexity, the encyclopedic ambitions of the project had to be moderated. Thus, a number of significant recent theoretical developments are barely touched upon here, or are merely sketched. For the same reason, it is not feasible to pres
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