Introduction to Inverse Problems for Differential Equations

Authors: Hasanov Hasanoğlu, Alemdar, Romanov, Vladimir G.

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  • First systematic and comprehensive introductory book on inverse problems for differential equations
  • Self-contained and accessible also to beginning graduate students
  • Can be used as a backbone for a lecture on inverse and ill-posed 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 self-contained 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 ill-posed problems for partial differential equations.

In turn, the second part of the book consists of six nearly-independent 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 well-written, easy-to-read, and basically self-contained survey on a wide range of inverse problems related with initial-boundary 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 self-study 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 state-of-the-art 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)

Table of contents (9 chapters)

Buy this book

eBook n/a
  • ISBN 978-3-319-62797-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-3-319-62796-0
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-3-319-87399-2
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Inverse Problems for Differential Equations
Authors
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-62797-7
DOI
10.1007/978-3-319-62797-7
Hardcover ISBN
978-3-319-62796-0
Softcover ISBN
978-3-319-87399-2
Edition Number
1
Number of Pages
XIII, 261
Number of Illustrations
4 b/w illustrations
Topics