Spectral Geometry and Inverse Scattering Theory
Description
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.
Reviews / Votes
"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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Huaian Diao is a Professor at School of Mathematics, Jilin University, China, from October 2021. He obtained his PhD in Mathematics from City University of Hong Kong (2007). From September 2007 to June 2021, he worked as a lecture and then an associate professor at School of Mathematics and Statistics, Northeast Normal University, China. His research interests include inverse scattering problems, numerical algebra and spectral theory. He has published over 50 peer-reviewed papers in international journals and conferences including J. Math. Pures Appl., Calc. Var. Partial Differential Equations, Comm. Partial Differential Equations, SIAM J. Math. Anal., SIAM J. Appl. Math., J. Differential Equations, Math. Comp., Inverse Problems, and NeurIPS 2019.
