An Introduction To Nonlinear Partial Differential Equations

An Introduction to NonlinearPartial Differential EquationsSecond EditionJ. David LoganWilla Cather Professor of MathematicsUniversity of Nebraska, LincolnDepartment of MathematicsLincoln, NEWI LEYINTERSCIENCEA JOHN WILEY & SONS, INC., PUBLICATION

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An Introduction to NonlinearPartial Differential Equations

PURE AND APPLIED MATHEMATICSA Wiley-Interscience Series of Texts, Monographs, and TractsFounded by RICHARD COURANTEditors Emeriti: MYRON B. ALLEN 111, DAVID A. COX, PETER HILTON,HARRY HOCHSTADT, PETER LAX, JOHN TOLANDA complete list of the titles in this series appears at the end of this volume.

An Introduction to NonlinearPartial Differential EquationsSecond EditionJ. David LoganWilla Cather Professor of MathematicsUniversity of Nebraska, LincolnDepartment of MathematicsLincoln, NEWI LEYINTERSCIENCEA JOHN WILEY & SONS, INC., PUBLICATION

Copyright 'C 2008 by John Wiley & Sons, Inc. All rights reserved.Published by John Wiley & Sons, Inc., Hoboken, h'ew JerseyPublished simultaneously in Canada.No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form orby any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except aspermitted under Section 107 or 108 of the 1976 United States Copyright Act. without either the priorIvritten permission of the Publisher, or authorization through payment of the appropriate per-copy fee tothe Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax(978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission shouldbe addressed to the Permissions Department, John Wiley & Sons, Inc., I 1 1 River Street, Hoboken, NJ07030, (201) 748-601 1, fax (201) 748-6008, or online at http://www.wiley.com/goipermission.Limit of Liability/Disclairner of Warranty: While the publisher and author have used their best efforts inpreparing this book, they make no representations or warranties with respect to the accuracy orcompleteness of the contents of this book and specifically disclaim any implied warranties ofmerchantability or fitness for a particular purpose. No warranty may be created or extended by salesrepresentatives or written sales materials. The advice and strategies contained herein may not be suitablefor your situation. You should consult with a professional where appropriate. Neither the publisher norauthor shall be liable for any loss of profit or any other commercial damages, including but not limitedto special, incidental, consequential, or other damages.For general information on our other products and services or for technical support, please contact ourCustomer Care Department within the United States at (800) 762-2974, outside the United States at(317) 572-3993 or fax (317) 572-4002.Wiley also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic format. For information about Wiley products, visit our web site atwww.wiley.com.Library of Congress Cataloging-in-Publication Data:Logan, J. David (John David)An introduction to nonlinear partial differential equations / J. David Logan. - 2nd ed.p. cm.Includes bibliographical references and index.ISBN 978-0-470-22595-0 (cloth : acid-free paper)1. Differential equations, Nonlinear. 2. Differential equations, Partial. I. Title.QA377.L58 20085 15'.353-d 222007047514Printed in the United States of America.10 9 8 7 6 5 4 3 2 1

To Tess, for all her aSfection und support

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ContentsPrefacexi1.Introduction t o Partial Differential Equations1.1 Partial Differential Equations1.1.1 Equations and Solutions1.1.2 Classification1.1.3 Linear versus Nonlinear1.1.4 Linear Equations1.2 Conservation Laws1.2.1 One Dimension1.2.2 Higher Dimensions1.3 Constitutive Relations1.4 Initial and Boundary Value Problems1.5 Waves1.5.1 Traveling Waves1.5.2 Plane TVaves1.5.3 Plane JYaves and Transforms1.5

Nonlinear partial differential equations (PDEs) is a vast area. and practition- ers include applied mathematicians. analysts. and others in the pure and ap- plied sciences. This introductory text on nonlinear partial differential equations evolved from a graduate course I have taught for many years at the University of Nebraska at Lincoln.