LEADER 03923nam 22005895 450 001 9910746969303321 005 20250604142714.0 010 $a9783031346156 010 $a3031346157 024 7 $a10.1007/978-3-031-34615-6 035 $a(MiAaPQ)EBC30764558 035 $a(Au-PeEL)EBL30764558 035 $a(DE-He213)978-3-031-34615-6 035 $a(PPN)27274011X 035 $a(CKB)28443810400041 035 $a(EXLCZ)9928443810400041 100 $a20230929d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSpectral Geometry and Inverse Scattering Theory /$fby Huaian Diao, Hongyu Liu 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (388 pages) 311 08$aPrint version: Diao, Huaian Spectral Geometry and Inverse Scattering Theory Cham : Springer,c2023 9783031346149 327 $aIntroduction. -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. 330 $aInverse 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. . 606 $aGeometry 606 $aDifferential equations 606 $aGeometry 606 $aDifferential Equations 606 $aGeometria espectral$2thub 606 $aTransformacions (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aGeometry. 615 0$aDifferential equations. 615 14$aGeometry. 615 24$aDifferential Equations. 615 7$aGeometria espectral 615 7$aTransformacions (Matemātica) 676 $a516 700 $aDiao$b Huaian$01431190 701 $aLiu$b Hongyu$01381763 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910746969303321 996 $aSpectral Geometry and Inverse Scattering Theory$93573307 997 $aUNINA