Overview
- 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
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (11 chapters)
-
Front Matter
-
Introduction to Inverse Problems
-
Front Matter
-
-
Inverse Problems for Differential Equations
-
Front Matter
-
-
Inverse Problems in Wave Phenomena and Vibration
-
Front Matter
-
-
Back Matter
Keywords
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.
Authors and Affiliations
Bibliographic Information
Book Title: Introduction to Inverse Problems for Differential Equations
Authors: Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
DOI: https://doi.org/10.1007/978-3-030-79427-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-79426-2Published: 03 August 2021
Softcover ISBN: 978-3-030-79429-3Published: 04 August 2022
eBook ISBN: 978-3-030-79427-9Published: 02 August 2021
Edition Number: 2
Number of Pages: XVII, 515
Number of Illustrations: 23 b/w illustrations, 5 illustrations in colour
Topics: Partial Differential Equations, Computational Science and Engineering, Numerical Analysis, Mathematics of Computing, Theoretical, Mathematical and Computational Physics