Functional Analytic Methods for Evolution Equations
This book consist of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for
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G. Da Prato A. Lunardi
P. C. Kunstmann I. Lasiecka R. Schnaubelt L. Weis
Functional Analytic Methods for Evolution Equations Editors: M. Iannelli R. Nagel S. Piazzera
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Authors Giuseppe Da Prato Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa, Italy e-mail: [email protected] Peer C. Kunstmann Lutz Weis Mathematisches Institut I Universit¨at Karlsruhe Englerstrasse 2 76128 Karlsruhe, Germany e-mail: [email protected] [email protected] Irena Lasiecka Department of Mathematics University of Virginia Kerchof Hall, P.O. Box 400137 Charlottesville VA 22904-4137, U.S.A. e-mail: [email protected] Alessandra Lunardi Department of Mathematics University of Parma via D’Azeglio 85/A 43100 Parma, Italy
Roland Schnaubelt FB Mathematik und Informatik Martin-Luther Universit¨at Theodor-Lieser-Str. 5 6099 Halle, Germany e-mail: [email protected]
Editors Mimmo Iannelli Department of Mathematics University of Trento via Sommarive 14 38050 Trento, Italy e-mail: [email protected] Rainer Nagel Susanna Piazzera Mathematisches Institut Universit¨at T¨ubingen Auf der Morgenstelle 10 72076 T¨ubingen, Germany e-mail: [email protected] [email protected]
e-mail: [email protected]
Library of Congress Control Number: 200411249 Mathematics Subject Classification (2000): 34Gxx, 34K30, 35K90, 42A45, 47Axx, 47D06, 47D07, 49J20, 60J25, 93B28 ISSN 0075-8434 ISBN 3-540-23030-0 Springer Berlin Heidelberg New York DOI: 10.1007/b100449 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm 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. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science + Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2004 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the authors 41/3142/du - 543210 - Printed on acid-free paper
Preface
Evolution equations describe time dependent processes as they occur in physics, biology, economy or other sciences. Mathematically, they appear in quite different forms, e.g., as parabolic or hyperbolic partial differential equations, as integrodifferential equations, as delay or difference differential equations or more general functional differential equations. While each class of equations has its own well established theory w
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