Optimal Control of Coupled Systems of Partial Differential Equations
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Honorary Editor: J. Todd, Pasadena †
Optimal Control of Coupled Systems of Partial Differential Equations
Karl Kunisch Günter Leugering Jürgen Sprekels Fredi Tröltzsch Editors
Birkhäuser Basel · Boston · Berlin
Editors: Karl Kunisch Institut für Mathematik und Wissenschaftliches Rechnen Universität Graz Heinrichstrasse 36 8010 Graz Austria Email: [email protected]
Günter Leugering LS Angewandte Mathematik II Institut für Angewandte Mathematik Universität Erlangen-Nürnberg Martensstrasse 3 91058 Erlangen Germany Email: [email protected]
Jürgen Sprekels Abt. Partielle Differentialgleichung Weierstraß-Institut für Angewandte Analysis und Stochastik Humboldt-Universität zu Berlin Mohrenstrasse 39 10117 Berlin Germany Email: [email protected]
Fredi Tröltzsch Institut für Mathematik Fak. II Mathematik & Naturwissenschaften TU Berlin Strasse des 17. Juni 136 10623 Berlin Germany Email: [email protected]
2000 Mathematics Subject Classification: Primary 49-XX, 35-XX; Secondary: 14J70, 26A16, 30F45, 35A15, 35B37, 35Bxx, 35D05, 35J85, 35L05, 35L55, 35L99, 35Q30, 35Q35, 35Q40, 47J40, 49J20, 65J15, 65K10, 49K20, 49L20, 65N15, 49Q10, 70K70, 72C02, 73K12, 74B05, 74K20, 74K25, 74K30, 74P05, 76D05, 76D07, 76N10, 76N15, 78A55, 80A20, 90C22, 90C25, 90C31, 90C90, 93A30, 93B05, 93B12, 93C20, 93D20, 93-XX, 76D55, 49K20, 49J20, 49K20, 35J65, 35B37, 93B05, 93B07 Library of Congress Control Number: 2009930314 Bibliographic information published by Die Deutsche Bibliothek. Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
ISBN 978-3-7643-8922-2 Birkhäuser Verlag AG, Basel - Boston - Berlin 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. For any kind of use permission of the copyright owner must be obtained. © 2009 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TCF ∞ Printed in Germany ISBN 978-3-7643-8922-2 987654321
e-ISBN 978-3-7643-8923-9 www.birkhauser.ch
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
G. Avalos, I. Lasiecka and R. Triggiani Beyond Lack of Compactness and Lack of Stability of a Coupled Parabolic-hyperbolic Fluid-structure System . . . . . . . . . . . . . . . .
1
C. Brandenburg, F. Lindemann, M. Ulbrich and S. Ulbrich A Continuous Adjoint Approach to Shape Optimization for Navier Stokes Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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E. Casas and F. Tr¨ oltzsch Recent Advances in the Analysis of State-constrained Elliptic Op
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