Differential Equations and Mathematical Physics Proceedings of an In

The meeting in Birmingham, Alabama, provided a forum for the discussion of recent developments in the theory of ordinary and partial differential equations, both linear and non-linear, with particular reference to work relating to the equations of mathema

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1285 I. W Knowles Y. Saito (Eds)

Differential Equations and Mathematical Physics Proceedings of an International Conference held in Birmingham, Alabama, USA, March 3-8, 1986

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann

1285 I. W Knowles Y. Saito (Eds)

Differential Equations and Mathematical Physics Proceedings of an International Conference held in Birmingham, Alabama, USA, March 3-8, 1986

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

Editors

Ian W. Knowles Yoshimi Saito Department of Mathematics, The University of Alabama at Birmingham Birmingham, AL 35294, USA

Mathematics Subject Classification (1980): 34, 35, 42, 73, 76, 78,81 ISBN 3-540-18479-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-18479-1 Springer-Verlag New York Berlin Heidelberg

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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.

© Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210

This volume is respectfully dedicated to Professor Tosio Kato on the occasion of his seventieth birthday.

PREFACE This volume forms a permanent record of lectures given at the International Conference on Differential Equations and Mathematical Physics held at the Universi ty of Alabama at Birmingham during March 3-8. 1986. The conference was supported by about 250 mathematicians from the following countries:

Belgium. Canada. Czechoslovakia. Denmark. Egypt. Finland. France.

Hungary. India. Ireland. Japan. Kuwait. Nigeria. Norway. P.R. of China. South Africa. Sweden. Switzerland. The Netherlands. the U.K.. the U.S.A .. and West Germany.

Its main purpose was to provide a forum for the discussion of recent

developments in the theory of ordinary and partial differential equations. both linear and non-linear. with particular reference to work relating to the equations of mathematical physics.

Invited one-hour lectures were given by P.

Deift. R. DiPerna. W.N. Everitt. C. Foias. T. Kato. S. Kotani. A. Majda. J. Mawhin. J. McLaughlin. J. McLeod. C. Morawetz. R. Newton. R. Phillips. M. Reed. I. Sigal. and B. Simon.

The remainder of the program consisted of invited

one-half hour lectures.

On behalf of the participants. the conference directors acknowledge. with gratitude. the generous financial support provided by the U.S. National Science Foundation. under grant number DMS-8516772. the Department of Mathematics and the Graduate School. University of Alabama at Birm