Overview
- The dynamical systems method (DSM) for solving operator equations, especially nonlinear and ill-posed
- Many novel results in the presentation of the theory of one-dimensional inverse problems
- Many novel results in the presentation of inverse obstacle scattering, including very weak assumptions on the smoothness of the obstacle, stability estimates for the solution, and an analysis of the earlier works
- A mathematically justified method, developed by the author for solving multidiemsional inverse potential scattering problem with fixed-energy data; error estimates
- A study of a non-overdetermined inverse problem
- Derivation of the analytical formulas for the S-matrix for eletromagnetic and acoustic wave scattering by small bodies of arbitrary shapes
- Discussion of the Pompeiu problem and the Schiffer's conjecture
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical and Analytical Techniques with Applications to Engineering (MATE)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (11 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
Reviews
From the reviews of the first edition:
"The author’s attention is addressed … to inverse problems for scattering theory … . the reviewer emphasizes the author’s effort of simplifying both the results in the mathematical literature and his own ones as well as the effort of unifying the theory of the inverse problems illustrated. Moreover, the proofs of the various propositions are almost always inserted in the book so that we can say the volume is friendly to readers … . Finally, the proofs are well written … ." (Alfredo Lorenzi, Zentralblatt MATH, Vol. 1083, 2006)
“This book is devoted to the investigation of inverse problems for PDEs, in particular, to the theory of inverse spectral problems and inverse scattering problems. … Graduate students and researchers will find in this work extensive reference material including a collection of relevant classical results as well as several new developments in the area of inverse and ill-posed problems.” (Antonio C. G. Leitão, Mathematical Reviews, Issue 2012 k)
Bibliographic Information
Book Title: Inverse Problems
Book Subtitle: Mathematical and Analytical Techniques with Applications to Engineering
Authors: Alexander G. Ramm
Series Title: Mathematical and Analytical Techniques with Applications to Engineering
DOI: https://doi.org/10.1007/b100958
Publisher: Springer New York, NY
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag US 2005
Hardcover ISBN: 978-0-387-23195-2Published: 16 December 2004
Softcover ISBN: 978-1-4419-3585-4Published: 19 November 2010
eBook ISBN: 978-0-387-23218-8Published: 19 December 2005
Series ISSN: 1559-7458
Series E-ISSN: 1559-7466
Edition Number: 1
Number of Pages: XX, 442
Topics: Mathematical and Computational Engineering, Applications of Mathematics, Theoretical, Mathematical and Computational Physics, Image Processing and Computer Vision, Ordinary Differential Equations