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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  • ISBN 978-3-030-79427-9
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Hardcover $169.99
price for USA in USD
  • ISBN 978-3-030-79426-2
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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.

For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition.


Table of contents (11 chapters)

Table of contents (11 chapters)
  • Introduction Ill-Posedness of Inverse Problems

    Pages 1-20

    Hasanov Hasanoğlu, Alemdar (et al.)

  • Functional Analysis Background of Ill-Posed Problems

    Pages 23-64

    Hasanov Hasanoğlu, Alemdar (et al.)

  • Inverse Source Problems with Final Overdetermination

    Pages 65-125

    Hasanov Hasanoğlu, Alemdar (et al.)

  • Inverse Problems for Hyperbolic Equations

    Pages 129-150

    Hasanov Hasanoğlu, Alemdar (et al.)

  • One-dimensional Inverse Problems in Electrodynamics

    Pages 151-170

    Hasanov Hasanoğlu, Alemdar (et al.)

Buy this book

eBook $129.00
price for USA in USD
  • ISBN 978-3-030-79427-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-3-030-79426-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Inverse Problems for Differential Equations
Authors
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-79427-9
DOI
10.1007/978-3-030-79427-9
Hardcover ISBN
978-3-030-79426-2
Edition Number
2
Number of Pages
XVII, 515
Number of Illustrations
23 b/w illustrations, 5 illustrations in colour
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