Linear Hyperbolic Equations
The present survey is devoted to the linear hyperbolic equations and systems. The concept of a hyperbolic equation first appeared in the case of a second-order equation $$Pu = \sum\limits_{i,j = 0}^n {{a_{ij}}} {\partial _i}{\partial _j}u = 0$$ (0.1) with
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Editor-in-Chief: R.V. Gamkrelidze
Yu.Y. Egorov M. A. Shubin (Eds.)
Partial Differential Equations IV Microlocal Analysis and Hyperbolic Equations
Springer-Verlag Berlin Heidelberg GmbH
Consulting Editors of the Series: A.A. Agrachev, A.A. Gonchar, E.F. Mishchenko, N.M. Ostianu, V.P. Sakharova, A.B. Zhishchenko
Title of the Russian edition: Itogi nauki i tekhniki, Sovremennye problemy matematiki, Fundamental'nye napravleniya, Vol. 33, Differentsial'nye uravneniya s chastnymi proizvodnymi 4 Publisher VINITI, Moscow 1988
Mathematics Subject Classification (1991): 35-02, 35Axx, 35A27, 35H05, 35Lxx, 35S30, 46Fxx, 47G30, 58G15,58G16, 58G17, 70Hxx ISBN 978-3-642-08099-9
Library of Congress Cataloging-in-Publication Data Differentsial'nye uravnenifii s chastnymi proizvodnymi 4. English Partial differential equations IV: microlocal analysis and hyperbolic equations/Yu.V. Egorov, M.A. Shubin. p. cm.-(Encyclopaedia of mathematical sciences; v. 33) Includes bibliographical references and indexes. ISBN 978-3-642-08099-9 ISBN 978-3-662-09207-1 (eBook) DOI 10.1007/978-3-662-09207-1 I. Mathematical analysis. 2. Differential equations, Hyperbolic. I. Egorov, ID. v. (IDrii Vladimirovich) II. Shubin, M.A. (Mikhail Aleksandrovich), 1944- . III. Title. IV. Title: Partial differential equations 4. V. Title: Partial differential equations four. VI. Series. QA300.D471513 1993 515'.353-dc20 92-22077 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under
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© Springer-Verlag Berlin Heidelberg 1993
Originally published by Springer-Verlag Berlin Heidelberg New York in 1993 Softcover reprint of the hardcover 1s1 edition 1993 Typesetting: Asco Trade Typesetting Ltd., Hong Kong 41/3140-54321O-Printed on acid-free paper
List of Editors, Authors and Translators Editor-in-Chief
R.V. Gamkrelidze, Russian Academy of Sciences, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Institute for Scientific Information (VINITI), ul. Usievicha 20a, 125219 Moscow, Russia Consulting Editors
Yu.V. Egorov, Department of Mathematics, Moscow State University, Leninskie Gory, 119899 Moscow, Russia M.A. Shubin, Department of Mathematics, Moscow State University, Leninskie Gory, 119899 Moscow, Russia Authors
Yu.V. Egorov, Department of Mathematics, Moscow State University, Leninskie Gory, 119899 Moscow, Russia v.Ya. Ivrii, Department of Mathematics, Magnitogorsk Mining-Metallurgical Institute, 455000 Magnitogorsk, Russia, and Department of Mathematics, University of Toronto, 100 St. George
