Lectures on Nonlinear Evolution Equations Initial Value Problems
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of loca
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Lectures on Nonlinear Evolution Equations Initial Value Problems Second Edition
Reinhard Racke
Lectures on Nonlinear Evolution Equations Initial Value Problems Second Edition
Reinhard Racke Department of Mathematics and Statistics University of Konstanz Konstanz, Germany
ISBN 978-3-319-21872-4 ISBN 978-3-319-21873-1 (eBook) DOI 10.1007/978-3-319-21873-1 Library of Congress Control Number: 2015948864 Mathematics Subject Classification (2010): 35B40, 35K05, 35K55, 35L05, 35L45, 35L70, 35Q99, 36Q60, 35Q74, 74F05 Springer Cham Heidelberg New York Dordrecht London First edition published by Vieweg, Wiesbaden, 1992 © Springer International Publishing Switzerland 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. Cover design: deblik, Berlin 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 the second edition of the book Lectures on nonlinear evolution equations. Initial value problems [150] from 1992. Additionally, it now includes a new Chapter 13 on initial-boundary value problems for waveguides, addressing more advanced students and researchers. Several people contributed helpful comments on the first edition and on the new Chapter 13. In particular I would like to thank Dipl.-Math. Karin Borgmeyer, Dr. Michael Pokojovy, Dipl.-Math. Marco Ritter, and Dipl.-Math. Alexander Sch¨owe. For typing Chapter 13 I thank Gerda Baumann. I am obliged to Birkh¨auser, in particular to Clemens Heine, for the interest in publishing this book.
Konstanz, April 2015
Reinhard Racke
Preface to the first edition: The book in hand is based on lectures which were given at the University of Bonn in the winter semesters of 1989/90 and 1990/91. The aim of the lectures was to present an elementary, self-contained introduction into some important aspects of the theory of global, small, smooth solutions to initial value problems for nonlinear evolution equations. The addressed audi
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