Front Tracking for Hyperbolic Conservation Laws
This is the second edition of a well-received book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions, and th
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Helge Holden Nils Henrik Risebro
Front Tracking for Hyperbolic Conservation Laws Second Edition
Applied Mathematical Sciences Founding Editors Fritz John, Joseph Laselle and Lawrence Sirovich
Editors S.S. Antman [email protected] Leslie Greengard [email protected] P.J. Holmes [email protected]
Advisors J. Bell P. Constantin J. Keller R. Kohn R. Pego L. Ryzhik A. Singer A. Stevens A. Stuart S. Wright
More information about this series at http://www.springer.com/series/34
Helge Holden Nils Henrik Risebro
Front Tracking for Hyperbolic Conservation Laws 2nd Edition
Helge Holden Department of Mathematical Sciences Norwegian University of Science and Technology Trondheim, Norway
Nils Henrik Risebro Department of Mathematics University of Oslo Oslo, Norway
ISSN 0066-5452 ISSN 2196-968X (electronic) Applied Mathematical Sciences ISBN 978-3-662-47506-5 ISBN 978-3-662-47507-2 (eBook) DOI 10.1007/978-3-662-47507-2 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2015956546 Mathematics Subject Classification (2010): 35Lxx, 35L65, 58J45 © Springer-Verlag Berlin Heidelberg 2002, 2015 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 Springer-Verlag GmbH Berlin Heidelberg is part of Springer Science+Business Media (www.springer.com)
In memory of Raphael, who started it all
Preface to the Second Edition
On general grounds I deprecate prefaces.1 — Winston Churchill
In this edition we have added the following new material: In Chapt. 1 we have added a section on linear equations, which allows us to present some of the material in the book in the simpler linear setting. In Chapt. 2 we have made some changes in the presentation of Kružkov’s fundamental doubling of variables method. In Chapt. 3 on finite difference methods the focus has been changed to finite volume methods. A section on higher-order schemes has been added. The section on measure-valued solutions has been rewritten. The main existence theo
