Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathemati
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P.L. SACHDEV CH. SRINIVASA RAO
Springer Monographs in Mathematics
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P.L. Sachdev · Ch. Srinivasa Rao
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
123
P.L. Sachdev (Deceased)
Ch. Srinivasa Rao Department of Mathematics Indian Institute of Technology Madras Sardar Patel Road Chennai-600036 India [email protected] [email protected]
ISSN 1439-7382 ISBN 978-0-387-87808-9 e-ISBN 978-0-387-87809-6 DOI 10.1007/978-0-387-87809-6 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009937490 Mathematics Subject Classification (2000): 35Kxx, 35Lxx, 35Qxx, 76xx c Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The present authors have been engaged in the study – both analytical and numerical – of large time asymptotic behaviour of nonlinear partial differential equations (PDEs) for many years. They had considerable interaction on this subject with Professor B. Enflo, KTH, Stockholm and Professor R. E. Grundy, University of St. Andrews, St. Andrews. Their contribution is gratefully acknowledged. The present venture was embarked upon while the first author (PLS) was Senior Scientist (Indian National Science Academy) at the Department of Mathematics, Indian Institute of Science, Bangalore, and was completed when he moved to the Department of Mathematics, University of Delhi, South Campus. He wishes to thank both the IISc and the University of Delhi for the facilities and to INSA for financial support. The second author (ChSR) is grateful to the Indian Institute of Technology Madras, Chennai for the financial support under Golden Jubilee book writing and new faculty schemes as he worked on this monograph. The authors also acknowledge the efforts of Professor K. T. Joseph, Tata Institute of Fundamental Research, Bombay and Mr. Manoj Kumar Yadav, IIT Madras, who carefully went through some parts of this book. New Delhi, Chennai August 2008
P. L. Sachdev Ch. Srinivasa Rao
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Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .
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