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International Series of Numerical Mathematics Volker Schulz Diaraf Seck Editors 169 Shape Optimization, Homogenization and Optimal Control DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 ISNM International Series of Numerical Mathematics Volume 169 Managing Editors G. Leugering, Erlangen, Germany M. Hintermueller, Berlin, Germany Associate Editors V. N. Starovoitov, Novosibirsk, Russia N. Kenmochi, Kita-ku, Kyoto, Japan R. W. Hoppe, Houston, USA Z. Chen, Beijing, China Honorary Editor K.-H. Hoffmann, Garching, Germany More information about this series at http://www.springer.com/series/4819 Volker Schulz • Diaraf Seck Editors Shape Optimization, Homogenization and Optimal Control DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 Editors Volker Schulz FB IV Abt. Mathematik Universit¨at Trier Trier, Germany Diaraf Seck Département de Mathématiques de la Université Cheikh Anta Diop de Daka Dakar-Fann, Senegal ISSN 0373-3149 ISSN 2296-6072 (electronic) International Series of Numerical Mathematics ISBN 978-3-319-90468-9 ISBN 978-3-319-90469-6 (eBook) https://doi.org/10.1007/978-3-319-90469-6 Library of Congress Control Number: 2018951124 Mathematics Subject Classification (2010): 49Q10, 35B27, 49J15, 49J20, 65K10 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface This volume contains the proceedings of the DFG-AIMS Workshop on shape optimization, homogenization and control, held at AIMS Sénégal in Mbour, Sénégal, on March 13–16, 2017. This workshop joined mathematicians from Sénégal, Germany and various other countries to discuss the topics of shape optimization, homogenization and control and to explore mutual interests and options of further joint research. The contributions in this volume give an insight into current research activities in Africa, Germany and internationally in those fields. Seeds for collaboration can be found in the first four papers in the field of homogenization. Modelling and optimal control in partial differential equations is the topic of the next six papers, again mixed from Africa and Germany. Finally, new results in the field of shape optimization are discussed in the final international three papers. This workshop has been supported by the Deutsche Forschungsgemeinschaft (DFG), which is the la