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roduction to Inverse Problems for Differential Equations

Introduction to Inverse Problems for Differential Equations

Alemdar Hasanov Hasanoğlu Vladimir G. Romanov

Introduction to Inverse Problems for Differential Equations

123

Vladimir G. Romanov Sobolev Institute of Mathematics Novosibirsk Russia

Alemdar Hasanov Hasanoğlu Department of Mathematics University of Kocaeli Izmit, Kocaeli Turkey

ISBN 978-3-319-62796-0 DOI 10.1007/978-3-319-62797-7

ISBN 978-3-319-62797-7

(eBook)

Library of Congress Control Number: 2017947470 Mathematics Subject Classification (2010): 65N21, 65F22, 35R25, 47J06, 47A52, 65R32, 65M32, 80A23 © Springer International Publishing AG 2017 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 Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

This book is dedicated to our wives, Şafak Hasanoğlu and Nina D. Romanova, who have been patient during all our lives together.

Preface

Mathematical models of the most physical phenomena are governed by initial and boundary value problems for partial differential equations (PDEs). Inverse problems governed by these equations arise naturally in almost all branches of science and engineering. The main objective of this textbook is to introduce students and researchers to inverse problems arising in PDEs. This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though we make no claim to cover all of the topics. More detailed additional information related to each chapter can be found in the following books/lecture notes/monographs of Aster, Borchers, and Thurber [2], Bal [6], Baunmeister [8], Beilina and Klibanov [9], Belishev and Blagovestch