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This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from…

Analysis of PDEs · Mathematics 2020-01-10 Isaac Harris , Dinh-Liem Nguyen , Jonathan Sands , Trung Truong

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…

Analysis of PDEs · Mathematics 2021-07-21 Shiqi Ma , Mikko Salo

In this paper we consider the inverse scattering problem at a fixed energy for the Schr\"odinger equation with a long-range potential in $\ere^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading…

Mathematical Physics · Physics 2020-05-22 Ricardo Weder , Dimitri Yafaev

The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…

Analysis of PDEs · Mathematics 2018-05-21 Samuel Cogar , David Colton , Peter Monk

A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Towards this pursuit we introduce…

Analysis of PDEs · Mathematics 2020-10-13 Samuel Cogar , Peter Monk

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove…

Spectral Theory · Mathematics 2021-11-01 Natalia P. Bondarenko , Vjacheslav A. Yurko

Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset \mathbb R^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be H\"older…

Analysis of PDEs · Mathematics 2015-07-29 Guanghui Hu , Mikko Salo , Esa V. Vesalainen

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…

Mathematical Physics · Physics 2017-10-12 Evgeny Lakshtanov , Boris Vainberg

This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…

Numerical Analysis · Mathematics 2025-10-13 Yu Sun , Bo Chen , Peng Gao , Qiuyi Li , Yao Sun

We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…

Analysis of PDEs · Mathematics 2020-05-05 Emilia Blåsten , Hongyu Liu

Assume that a bounded scatterer is embedded into an infinite homogeneous isotropic background medium in two dimensions. The refractive index function is supposed to be piecewise constant. If the scattering interface contains a weakly or…

Analysis of PDEs · Mathematics 2018-01-15 Long Li , Guanghui Hu , Jiansheng Yang

We consider an inverse spectral theory in a domain with the cavity that is bounded by a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the solutions inside and outside the cavity. The ODE system is connected…

Analysis of PDEs · Mathematics 2016-05-18 Lung-Hui Chen

We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…

Optics · Physics 2012-08-23 Johannes Skaar , Magnus W. Haakestad

Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville…

Analysis of PDEs · Mathematics 2012-04-26 Lung-Hui Chen

The perturbative treatment of high-energy fixed-angle hadron-hadron exclusive scattering is reviewed and related to the transverse structure of the proton and other hadrons.

Nuclear Theory · Physics 2017-08-23 George Sterman

We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by…

Analysis of PDEs · Mathematics 2021-11-03 Cristóbal J. Meroño , Leyter Potenciano-Machado , Mikko Salo

This paper is concerned with inverse scattering problems of determining the support of an isotropic and homogeneous penetrable body from knowledge of multi-static far-field patterns in acoustics and in linear elasticity. The normal…

Analysis of PDEs · Mathematics 2024-04-11 Chun Liu , Guanghui Hu , Jianli Xiang , Jiayi Zhang

A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…

Mathematical Physics · Physics 2007-05-23 Alexander G. Ramm

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

Analysis of PDEs · Mathematics 2025-07-02 Jianliang Li , Peijun Li , Xu Wang , Guanlin Yang