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Spectral geometry and inverse scattering theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spectral geometry and inverse scattering theoryby Huaian Diao, Hongyu Liu.
Author:	Diao, Huaian.
other author:	Liu, Hongyu.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	x, 387 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Spectral geometry.
Online resource:	https://doi.org/10.1007/978-3-031-34615-6
ISBN:	9783031346156$q(electronic bk.)

Spectral geometry and inverse scattering theory
Diao, Huaian.

Spectral geometry and inverse scattering theory[electronic resource] /by Huaian Diao, Hongyu Liu. - Cham :Springer Nature Switzerland :2023. - x, 387 p. :ill. (some col.), digital ;24 cm.

Introduction. -Geometric structures of Laplacian eiegenfunctions -- Geometric structures of Maxwellian eigenfunctions -- Inverse obstacle and diffraction grating scattering problems -- Path argument for inverse acoustic and electromagnetic obstacle scattering problems -- Stability for inverse acoustic obstacle scattering problems. - Stability for inverse electromagnetic obstacle scattering problems -- Geometric structures of Helmholtz's transmission eigenfunctions with general transmission conditions and applications -- Geometric structures of Maxwell's transmission eigenfunctions and applications -- Geometric structures of Lame's transmission eigenfunctions with general ' transmission conditions and applications -- Geometric properties of Helmholtz's transmission eigenfunctions induced by curvatures and applications. - Stable determination of an acoustic medium scatterer by a single far-field pattern -- Stable determination of an elastic medium scatterer by a single far-field measurement and beyond.

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 reference source for researchers in acquiring the state-of-the-art results in inverse scattering theory and their potential applications.

ISBN: 9783031346156$q(electronic bk.)

Standard No.: 10.1007/978-3-031-34615-6doiSubjects--Topical Terms:

468049
Spectral geometry.

LC Class. No.: QA614.95 / .D53 2023

Dewey Class. No.: 516.362

Spectral geometry and inverse scattering theory
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505 0 $a Introduction. -Geometric structures of Laplacian eiegenfunctions -- Geometric structures of Maxwellian eigenfunctions -- Inverse obstacle and diffraction grating scattering problems -- Path argument for inverse acoustic and electromagnetic obstacle scattering problems -- Stability for inverse acoustic obstacle scattering problems. - Stability for inverse electromagnetic obstacle scattering problems -- Geometric structures of Helmholtz's transmission eigenfunctions with general transmission conditions and applications -- Geometric structures of Maxwell's transmission eigenfunctions and applications -- Geometric structures of Lame's transmission eigenfunctions with general ' transmission conditions and applications -- Geometric properties of Helmholtz's transmission eigenfunctions induced by curvatures and applications. - Stable determination of an acoustic medium scatterer by a single far-field pattern -- Stable determination of an elastic medium scatterer by a single far-field measurement and beyond.
520 $a 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 reference source for researchers in acquiring the state-of-the-art results in inverse scattering theory and their potential applications.
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650 0 $a Inverse scattering transform. $3 229168
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