The L1 Theory of the Scalar Conservation Law
The theory of the scalar balance law has reached a state of virtual completeness. In the framework of classical solutions, the elementary, yet effective, method of characteristics yields a sharper version of Theorem 5.1.1, determining explicitly the life
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Editors S. S. Chern B. Eckmann P. de la Harpe H. Hironaka F. Hirzebruch N. Hitchin L. Hormander M.-A. Knus A. Kupiainen J. Lannes G. Lebeau M. Ratner D. Serre Ya.G. Sinai N.J. A. Sloane J.Tits M. Waldschmidt S. Watanabe
Managing Editors M. Berger J. Coates S.R.S. Varadhan
Springer-Verlag Berlin Heidelberg GmbH
Constantine M. Dafermos
Hyperbolic Conservation Laws in Continuum Physics With 38 Figures
Springer
Constantine M. Dafermos Division of Applied Mathematics Brown University Providence, RI 02912 USA e-mail: [email protected]
Library of Congress Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Dafermos, Constantine M.: Hyperbolic conservation laws in continuum physics / Constantine M. Dafermos. (Grundlehren der mathematischen Wissenschaften; 325) ISBN 978-3-662-22021-4 DOI 10.1007/978-3-662-22019-1
ISBN 978-3-662-22019-1 (eBook)
Mathematics Subject Classification (1991): 35L65,35 L67,73Bxx,76L05
ISSN 0072-7830 ISBN 978-3-662-22021-4 This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically the rights of tra nslation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this pllblication 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-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 2000 Originally published by Springer-Verlag Berlin Heidelberg New York 2000 Softcover reprint of the hardcover lst edition 2000 Cover design: MetaDesign plus GmbH, Berlin Photocomposed from the allthor's TEX files after editing and reformatting by Kurt Mattes, Heidelberg, using the MathTime fonts and a Springer TEX macro-package Printed on acid-free paper SPIN: 10690815 41/3143Ko-5 43210
For Mihalis and Thalia
The universe is a gigantic system of reflexes produced by shocks. Bernard Shaw ("The black girl in search of God")
Preface
The seeds of Continuum Physics were planted with the works of the natural philosophers of the eighteenth century, most notably Euler; by the mid-nineteenth century, the trees were fully grown and ready to yield fruit. It was in this environment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called "hyperbolic conservation laws"; and these two subjects have been traveling hand-in-hand over the past one hundred and fifty years. This book aims at presenting the theory of hyperbolic conservation laws from the standpoint of its genetic relation to Continuum Physics. Even though research is still marching at a brisk pace, both fields have attained by now the degree of maturity that would warrant the writing of such an exposition. In the realm of Continuum Physics, material bodies are r
