Nonlinear Partial Differential Equations for Scientists and Engineers
An exceptionally complete overview of the latest developments in the field of PDEs. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. —Applied Mechan
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Nonlinear Partial Differential Equations for Scientists and Engineers Third Edition
Lokenath Debnath Department of Mathematics University of Texas, Pan American 1201 W. University Drive Edinburg, TX, 78539 USA [email protected]
ISBN 978-0-8176-8264-4 e-ISBN 978-0-8176-8265-1 DOI 10.1007/978-0-8176-8265-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011940003 Mathematics Subject Classification (2010): 00A06, 00A69, 33Exx, 33E12, 34B05, 34B24, 34B27, 34B60, 34G20, 34G25, 35A15, 35A21, 35A22, 35A25, 35C05, 35C15, 35Dxx, 35E05, 35E15, 35Fxx, 35F05, 35F10, 35F15, 35F20, 35F25, 35G10, 35G20, 35G25, 35J05, 35J10, 35J15, 35J20, 35K05, 35K10, 35K15, 35K55, 35K60, 35L05, 35L10, 35L15, 35L20, 35L25, 35L30, 35L60, 35L65, 35L67, 35L70, 35Q30, 35Q35, 35Q40, 35Q51, 35Q53, 35Q55, 35Q60, 42A38, 44A10, 44A35, 49J40, 49Lxx, 58E30, 58E50, 65L15, 65M25, 65M30, 65R10, 70H05, 70H06, 70H09, 70H20, 70H25, 70H30, 76Bxx, 76B07, 76B15, 76B25, 76B55, 76B60, 76B65, 76D05, 76D33, 76D45, 76E30, 76M30, 76R50, 78M30, 81Q05, 81Q10 © Springer Science+Business Media, LLC 2012 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.birkhauser-science.com)
TO MY MOTHER with love, gratitude, and admiration
True Laws of Nature cannot be linear. Albert Einstein . . . the progress of physics will to a large extent depend on the progress of nonlinear mathematics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. Werner Heisenberg Our present analytical methods seem unsuitable for the solution of the important problems arising in connection with nonlinear partial differential equations and, in fact, with virtually all types of nonlinear problems in pure mathematics. The truth of this statement is particularly striking in the field of fluid dynamics. . . . John Von Neumann However varied may be the imagination of man, nature is a thousand times richer, . . . Each of the theories of physics . . . presents (partial differential) equations under a new aspect . . . without these theories, we should not know partial differential equations. Henri Poincaré Since a general solution must be judged impossible from want of analysis, we must be content with the knowledge of some special cases, and that all the more, sinc
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