Introduction to Inverse Problems for Differential Equations
Authors: Hasanov Hasanoğlu, Alemdar, Romanov, Vladimir G.
Free Preview First systematic and comprehensive introductory book on inverse problems for differential equations
 Selfcontained and accessible also to beginning graduate students
 Can be used as a backbone for a lecture on inverse and illposed problems for partial differential equations
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 About this book

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering.
The book’s content, especially in the Introduction and Part I, is selfcontained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and illposed problems for partial differential equations.
In turn, the second part of the book consists of six nearlyindependent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties.
 Reviews

“This monograph provides a wellwritten, easytoread, and basically selfcontained survey on a wide range of inverse problems related with initialboundary problems for partial deferential equations. It addresses many relevant topics in the theory of such problems, with a focus on existence, uniqueness and stability of inverse coefficient and source problems. … The text can be used for selfstudy and will be of interest to experts in the field as well as graduate students.” (Boris Rubin, zbMATH 1385.65053, 2018)
“This book is an important contribution to the theory of inverse problems. It gives a complete picture of inverse problems and their applications. … It is a good research monograph for people working on inverse problems and related issues; a useful stateoftheart reference guide for researchers and students; and a fine textbook for graduate students in mathematics and engineering.” (Srinivasan Natesan, Computing Reviews, September, 2018)
 Table of contents (9 chapters)


Introduction IllPosedness of Inverse Problems for Differential and Integral Equations
Pages 119

Functional Analysis Background of IllPosed Problems
Pages 2362

Inverse Source Problems with Final Overdetermination
Pages 63119

Inverse Problems for Hyperbolic Equations
Pages 123143

OneDimensional Inverse Problems for Electrodynamic Equations
Pages 145162

Table of contents (9 chapters)
 Download Preface 1 PDF (69.8 KB)
 Download Sample pages 2 PDF (435.1 KB)
 Download Table of contents PDF (135.3 KB)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Introduction to Inverse Problems for Differential Equations
 Authors

 Alemdar Hasanov Hasanoğlu
 Vladimir G. Romanov
 Copyright
 2017
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing AG
 eBook ISBN
 9783319627977
 DOI
 10.1007/9783319627977
 Hardcover ISBN
 9783319627960
 Softcover ISBN
 9783319873992
 Edition Number
 1
 Number of Pages
 XIII, 261
 Number of Illustrations
 4 b/w illustrations
 Topics