English
Related papers

Related papers: Uniqueness in potential scattering with reduced ne…

200 papers

This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), by utilizing spectral properties of the…

Analysis of PDEs · Mathematics 2018-06-26 Xiaoxu Xu , Bo Zhang , Haiwen Zhang

Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be…

Analysis of PDEs · Mathematics 2018-12-26 Pedro Caro , Tapio Helin , Antti Kujanpää , Matti Lassas

We study the inverse scattering problem for electric potentials and magnetic fields in $\ere^d, d\geq 3$, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from…

Mathematical Physics · Physics 2009-11-11 Ricardo Weder , Dimitri Yafaev

A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…

Analysis of PDEs · Mathematics 2011-09-21 Masaru Ikehata

This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…

Analysis of PDEs · Mathematics 2017-06-14 Jiaqing Yang , Bo Zhang , Haiwen Zhang

The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is…

Analysis of PDEs · Mathematics 2014-01-03 Sebastian Acosta , Sum Chow , James Taylor , Vianey Villamizar

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.

Analysis of PDEs · Mathematics 2019-06-24 Manmohan Vashisth

We study the inverse scattering from a screen with using only one incoming time--harmonic plane wave but with measurements of the scattered wave done at all directions. Especially we focus on the 2D--case i.e. (inverse) scattering from an…

Analysis of PDEs · Mathematics 2024-09-05 Emilia Blåsten , Petri Ola , Lassi Päivärinta

In this paper, we study time-harmonic electromagnetic scattering in two scenarios, where the anomalous scatterer is either a pair of electromagnetic sources or an inhomogeneous medium, both with compact supports. We are mainly concerned…

Analysis of PDEs · Mathematics 2022-04-07 Huaian Diao , Xiaoxu Fei , Hongyu Liu , Ke Yang

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocusing case, we prove that arbitrary initial data in the energy space lead to global solutions that…

Analysis of PDEs · Mathematics 2020-06-23 Changxing Miao , Jason Murphy , Jiqiang Zheng

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

Analysis of PDEs · Mathematics 2009-12-16 Xiaodong Liu , Bo Zhang

It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always…

Analysis of PDEs · Mathematics 2021-12-03 Long Li , Guanghui Hu , Jiansheng Yang

We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and…

Mathematical Physics · Physics 2013-06-18 Alexandre Jollivet

Inverse scattering theory is extended to one-dimensional Schr\"odinger problems with near-boundary singularities of the form $v(z\to 0)\simeq -z^{-2}/4+v_{-1}z^{-1}$. Trace formulae relating the boundary value $v_0$ of the nonsingular part…

Mathematical Physics · Physics 2015-08-25 Sergei B. Rutkevich , H. W. Diehl

In this paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…

Analysis of PDEs · Mathematics 2023-05-16 Hongyu Liu , Shiqi Ma

Let $A_q(\alpha',\alpha,k)$ be the scattering amplitude, corresponding to a local potential $q(x)$, $x\in\R^3$, $q(x)=0$ for $|x|>a$, where $a>0$ is a fixed number, $\alpha',\alpha\in S^2$ are unit vectors, $S^2$ is the unit sphere in…

Mathematical Physics · Physics 2016-09-07 A. G. Ramm

In this paper, we consider the direct and inverse problem of scattering of time-harmonic waves by an unbounded rough interface with a buried impenetrable obstacle. We first study the well-posedness of the direct problem with a local source…

Analysis of PDEs · Mathematics 2017-01-09 Yulong Lu , Bo Zhang

We numerically investigate the sensitivity of the scattered wave field to perturbations in the shape of a scattering body illuminated by an incident plane wave. This study is motivated by recent work on the inverse problem of reconstructing…

Numerical Analysis · Mathematics 2025-03-14 Erik García Neefjes , Stuart C. Hawkins

This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…

Analysis of PDEs · Mathematics 2021-02-16 Jianliang Li , Peijun Li , Xu Wang

It is proved that a connected polygonal obstacle coated by thin layers together with its surface impedance function can be determined uniquely from the far field pattern of a single incident plane wave. Our proof is based on the Schwarz…

Analysis of PDEs · Mathematics 2020-09-11 Guang-Hui Hu , Manmohan Vashisth