Inverse acoustic and electromagnetic scattering theory.
type: Item
instance of: scholarly article
title: Inverse acoustic and electromagnetic scattering theory.
zbMATH Open document ID: 0893.35138
author: David Colton
author: Rainer Kress
published in: Applied Mathematical Sciences
publication date: 1998-01-22T00:00:00Z
review text: The first edition of this well-known and appreciated text, extremely valuable for both, students and researchers, appeared in 1992 (for a review cf. Zbl 0760.35053). The book consists of the following 10 Chapters: 1) Introduction, 2) The Helmholtz equation, 3) Direct acoustic obstacle scattering, 4) Ill-posed problems, 5) Inverse acoustic obstacle scattering, 6) The Maxwell equations, 7) Inverse electromagnetic obstacle scattering, 8) Acoustic waves in an inhomogeneous medium, 9) Electromagnetic waves in an inhomogeneous medium, 10) The inverse medium problem. Concerning the improvements, compared to the first edition, let the reviewer cite from the authors' Preface: ``In addition to making minor corrections and additional comments in the text and updating the references, we have added new sections on: Newton's method for solving the inverse obstacle problem (Section 5.3), the spectral theory of the far field operator (Section 8.4), a proof of the uniqueness of the solution to the inverse medium problem for acoustic waves (Section 10.2), and a method for determining the support of an inhomogeneous medium from far field data by solving a linear integral equation of the first kind (Section 10.7). We hope that this second edition will attract new readers to the beautiful and intriguing field of inverse scattering''.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 45A05
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 65R30
Mathematics Subject Classification ID: 76Q05
zbMATH DE Number: 1108876
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: acoustic obstacle scattering
zbMATH Keywords: Maxwell equations
zbMATH Keywords: electromagnetic obstacle scattering
zbMATH Keywords: waves in an inhomogeneous medium
zbMATH Keywords: inverse medium problem
zbMATH Keywords: Newton's method
zbMATH Keywords: uniqueness
zbMATH Keywords: far field data
zbMATH Keywords: linear integral equation of the first kind
reviewed by: Gottfried Bruckner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1108876