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Exploring the Essential Features of “Alexander Ramm – Inverse Problems”
Inverse Problems
Mathematical and Analytical Techniques with Applications to Engineering
Authors: Alexander G. Ramm
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
Table of contents (11 chapters)
Introduction
Methods of Solving Ill-Posed Problems
One-Dimensional Inverse Scattering and Spectral Problems
Inverse Obstacle Scattering
Stability of the Solutions to 3D Inverse Scattering Problems with Fixed-Energy Data
Non-Uniqueness and Uniqueness Results
Inverse Problems of Potential Theory and Other Inverse Source Problems
Non-Overdetermined Inverse Problems
Low-Frequency Inversion
Wave Scattering by Small Bodies of Arbitrary Shapes
The Pompeiu Problem
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)
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