Partial Differential Equations: Modeling, Analysis and Numerical Approximation
This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for
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168 Hervé Le Dret Brigitte Lucquin
Partial Differential Equations: Modeling, Analysis and Numerical Approximation
ISNM International Series of Numerical Mathematics Volume 168 Managing Editor G. Leugering, Erlangen-Nürnberg, Germany Associate Editors Z. Chen, Beijing, China R.H.W. Hoppe, Augsburg, Germany; Houston, USA N. Kenmochi, Chiba, Japan V. Starovoitov, Novosibirsk, Russia Honorary Editor K.-H. Hoffmann, München, Germany
More information about this series at www.birkhauser-science.com/series/4819
Hervé Le Dret Brigitte Lucquin •
Partial Differential Equations: Modeling, Analysis and Numerical Approximation
Hervé Le Dret Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie—Paris VI Paris France
Brigitte Lucquin Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie—Paris VI Paris France
ISSN 0373-3149 ISSN 2296-6072 (electronic) International Series of Numerical Mathematics ISBN 978-3-319-27065-4 ISBN 978-3-319-27067-8 (eBook) DOI 10.1007/978-3-319-27067-8 Library of Congress Control Number: 2015955864 Mathematics Subject Classification (2010): 35J20, 35J25, 35K05, 35K20, 35L03, 35L05, 65M06, 65M08, 65M12, 65N30 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 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 Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.birkhauser-science.com)
Preface
This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. A partial differential equation (PDE) is a relation between the partial derivatives of an unknown function u in several ou variables to be satisfied by this function, for example ou ot ox ¼ 0, where u is a function in the two variables t and x. Partial differential equations constitute a major field of study in contemporary mathematics. They also arise in other fields of mathematics, such as differe
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