Differential Equations in Banach Spaces Proceedings of a Conference
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1223 Differential Equations in Banach Spaces Proceedings of a Conference held in Bologna, July 2-5, 1985
Edited by A. Favini and E. Obrecht
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Editors
Angelo Favini Enrico Obrecht Dipartimento di Matematica, Universita di Bologna Piazzadi Porta S. Donato 5, 40127 Bologna, Italy
Mathematics Subject Classification (1980): 34G10, 34G20, 45N05, 47D05, 47E05,47G05 ISBN 3-540-17191-6 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-17191-6 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 those of translation, reprinting. re-use of illustrations, broadcasting. reproduction by photocopying machine or similar means. and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© Springer-Verlag Berlin Heidelberg 1986 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
FOREWORD
This volume contains most contributions to the conference on "DIFFERENTIAL EQUATIONS IN BANACH SPACES", which was held in the Department of Mathematics of the University of Bologna, July 25, 1985. The aim of the meeting was to stimulate the exchange of ideas and informations in this very rapidly developing field. The contributors, coming from several european countries, Japan and U.S.A., were specialists in different branches of abstract differential equations, so that the conference gave a panorama of different directions of research. Among the topics included are: regular and singular evolution equations both linear and nonlinear of parabolic and hyperbolic type, integrodifferential equations, semigroup theory, control theory, wave equations, trasmutation methods, fuchsian differential equations. During the meeting 23 one hour lectures and 7 short communications took place; 24 of these contributions appear now in this volume, some of them in an enlarged version. We have pleasure in thanking all participants in the meeting, whose active interest made this conference a success. We are also pleased to thank the instl tutions which made this meeting possible by their financial support: the
Consiglio Nazionale delle Ricerche Comitato per le Scienze Matematiche, the Ministero della Pubblica Istruzione (fondi 40%) and the University of Bologna. Finally, we are particularly grateful to those who helped, by their cooperation, and advice, the organization of the meeting and the editing of these proceedings: Giuseppe DA PRATO, Giovanni DORE, Davide GUIDETTI, Eugenio SINESTRARI and, last but not least, Alberto VENNI.
CONTENTS P. Acquistapace - B. Terreni: On Fundamental Solutions for Abstract Parabolic Equations
p.
1
M.L. Bernardi: On Some Singular Nonlinear Evolution Equations
p.
12
R. Carroll:
p.
25
p.
37
p.
49
W. Desch - W. Schappacher: Linearized Stability for Nonlinear Semigroups p. 1 G. D
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