Spectral Geometry and Inverse Scattering Theory / by Huaian Diao, Hongyu Liu.

Format:

Book

Author/Creator:

Diao, Huaian.

Contributor:

Liu, Hongyu.

Series:

Mathematics and Statistics Series

Language:

English

Subjects (All):

Geometry.

Differential equations.

Differential Equations.

Local Subjects:

Geometry.

Differential Equations.

Physical Description:

1 online resource (388 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2023.

Summary:

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. .

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Diao, Huaian Spectral Geometry and Inverse Scattering Theory

ISBN:

9783031346156

3031346157

OCLC:

1402179128