Spectral Geometry and Inverse Scattering Theory
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Beschreibung
Inverse scattering problems are a vital subject for both theoretical and experimental studies and remain an active field of research in applied mathematics. This book provides a detailed presentation of typical setup of inverse scattering problems for time-harmonic acoustic, electromagnetic and elastic waves. Moreover, it provides systematical and in-depth discussion on an important class of geometrical inverse scattering problems, where the inverse problem aims at recovering the shape and location of a scatterer independent of its medium properties. Readers of this book will be exposed to a unified framework for analyzing a variety of geometrical inverse scattering problems from a spectral geometric perspective.
This book contains both overviews of classical results and update-to-date information on latest developments from both a practical and theoretical point of view. It can be used as an advanced graduate textbook in universities or as a referencesource for researchers in acquiring the state-of-the-art results in inverse scattering theory and their potential applications.
Inverse scattering problems are a vital subject for both theoretical and experimental studies and remain an active field of research in applied mathematics. This book provides a detailed presentation of typical setup of inverse scattering problems for time-harmonic acoustic, electromagnetic and elastic waves. Moreover, it provides systematical and in-depth discussion on an important class of geometrical inverse scattering problems, where the inverse problem aims at recovering the shape and location of a scatterer independent of its medium properties. Readers of this book will be exposed to a unified framework for analyzing a variety of geometrical inverse scattering problems from a spectral geometric perspective.
This book contains both overviews of classical results and update-to-date information on latest developments from both a practical and theoretical point of view. It can be used as an advanced graduate textbook in universities or as a referencesource for researchers in acquiring the state-of-the-art results in inverse scattering theory and their potential applications.
Comprehensive treatment of inverse scattering problems; associates with acoustic, electromagnetic & elastic waves Includes discussions on the geometrical inverse shape problems by minimal measurements Develops perspective on inverse scattering theory from a spectral geometric viewpoint
Autor*in
Huaian Diao
Themen in »Spectral Geometry and Inverse Scattering Theory«
Wave scattering acoustics electromagnetism elastodynamics inverse shape problems single measurements uniqueness stability spectral geometry geometric structures of eigenfunctions
Stimmen zu »Spectral Geometry and Inverse Scattering Theory«
“The book under review provides an overview of certain modern topics in inverse scattering theory studied by the authors and their coauthors. In particular, the book is focussed on the geometric structure of eigenfunctions for several spectral problems … . Researchers working in this area will appreciate this book as a reference for these selected topics with most chapters being relatively self-contained.” (Joe Thomas, zbMATH 1543.58001, 2024)
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