EDITORIAL COMMITTEE David Cox (Chair) Rafe Mazzeo Martin Scharlemann Gigliola Staffilani 2010 Mathematics Subject Classification. Primary 35A18, 35A21, 35A27, 35A30, 35Q31, 35Q60, 78A05, 78A60, 78M35, 93B07. For additional information and updates on this book, visit www.ams.org/bookpages/gsm-133 Library of Congress Cataloging-in-Publication Data Rauch, Jeffrey. Hyperbolic partial differential equations and geometric optics / Jeffrey Rauch. p. cm. (Graduate studies in mathematics v. 133) Includes bibliographical references and index. ISBN 978-0-8218-7291-8 (alk. paper) 1. Singularities (Mathematics). 2. Microlocal analysis. 3. Geometrical optics—Mathematics. 4. Differential equations, Hyperbolic. I. Title. QC20.7.S54R38 2012 535 .32—dc23 2011046666 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA. Requests can also be made by e-mail to reprint-permission@ams.org. c 2012 by Jeffrey Rauch. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ 10 9 8 7 6 5 4 3 2 1 17 16 15 14 13 12
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