| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910746969303321 |
|
|
Autore |
Diao Huaian |
|
|
Titolo |
Spectral Geometry and Inverse Scattering Theory / / by Huaian Diao, Hongyu Liu |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
|
|
Edizione |
[1st ed. 2023.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (388 pages) |
|
|
|
|
|
|
Altri autori (Persone) |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Geometry |
Differential equations |
Differential Equations |
Geometria espectral |
Transformacions (Matemàtica) |
Llibres electrònics |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Nota di contenuto |
|
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. |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
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. . |
|
|
|
|
|
| |