Authors:
- 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
- Includes supplementary material: sn.pub/extras
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (9 chapters)
-
Front Matter
-
Introduction to Inverse Problems
-
Front Matter
-
-
Inverse Problems for Differential Equations
-
Front Matter
-
-
Back Matter
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 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)
Authors and Affiliations
-
Department of Mathematics, University of Kocaeli, Izmit, Turkey
Alemdar Hasanov Hasanoğlu
-
Sobolev Institute of Mathematics, Novosibirsk, Russia
Vladimir G. Romanov
Bibliographic Information
Book Title: Introduction to Inverse Problems for Differential Equations
Authors: Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
DOI: https://doi.org/10.1007/978-3-319-62797-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-87399-2Published: 07 August 2018
eBook ISBN: 978-3-319-62797-7Published: 31 July 2017
Edition Number: 1
Number of Pages: XIII, 261
Number of Illustrations: 4 b/w illustrations
Topics: Partial Differential Equations, Computational Science and Engineering, Numerical Analysis, Mathematics of Computing, Theoretical, Mathematical and Computational Physics