Nonlinear Semigroups, Partial Differential Equations and Attractors

The original idea of the organizers of the Washington Symposium was to span a fairly narrow range of topics on some recent techniques developed for the investigation of nonlinear partial differential equations and discuss these in a forum of experts. It s

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1248 Nonlinear Semigroups, Partial Differential Equations and Attractors Proceedings of a Symposium held in Washington, D.C., August 5-8, 1985

Edited by T. L. Gill and W. W. Zachary

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

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

1248 Nonlinear Semigroups, Partial Differential Equations and Attractors Proceedings of a Symposium held in Washington, D.C., August 5-8, 1985

Edited by T. L. Gill and W. W. Zachary

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

Editors

Tepper L. Gill Department of Electrical Engineering Howard University Washington, D. C. 20059, USA Woodford W. Zachary Naval Research Laboratory Washington, D. C. 20375, USA

Mathematics Subject Classification (1980): 34C35, 35A07, 35B30, 35K55, 35K57, 35K60, 35Q20, 47D05, 47H20 ISBN 3-540-17741-8 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-17741-8 Springer-Verlag New York Berlin Heidelberg

Library of Congress Cataloging-in-Publication Data. Nonlinear semigroups, partial differential equations, and attractors, (Lecture notes in mathematics; 1248) "Proceedings of the Symposium on Nonlinear Semigroups, Partial Differential Equations, and Attractors held at Howard University in Washington, D.C,"Pref. Bibliography: p. 1. Semigroups of operators-Congresses. 2. Differential equations, PartialCongresses. 3, Nonlinear operators-Congresses. 4. Differentiable dynamical systems-Congresses. I. Gill, T.L. (TepperL.), 1941-. II. Zachary. W. W .• 1935-.111. Symposium on NonlinearSemigroups, Partial Differential Equations. and Attractors (1985: Howard University) IY. Series: Lecture Notes in mathematics (Springer-Yerlag); 1248. 0A3.L28 no. 1248 [OA329,8j 510 s [515.7'248] 87-9448 ISBN 0-387-17741-8 (U.S,) 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-Yerlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210

PREFACE

This volume constitutes the proceedings of the Symposium on Nonlinear Semi groups , Partial Differential Equations, and Attractors held at Howard University in Washington. D.C. on August 5-8, 1985. This symposium was sponsored by a special grant from the President of Howard University. Dr, James E. Cheek.

The original intention of

the symposium organizers was to include a fairly narrow range of featured topics by a group of experts on some recent techniques developed for the investigation of nonlinear partial differential equations.

However. it soon bec