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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

We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…

Analysis of PDEs · Mathematics 2019-04-09 J Liu , X. Liu , J. Sun

We consider inverse potential scattering problems where the source of the incident waves is located on a smooth closed surface outside of the inhomogeneity of the media. The scattered waves are measured on the same surface at a fixed value…

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

Uniqueness theorems are proved for 3-d inverse scattering problems in the frequency domain under the assumption that only the modulus of the complex valued wave field is measured, while the phase is unknown.

Mathematical Physics · Physics 2013-03-06 Michael V. Klibanov

We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…

Analysis of PDEs · Mathematics 2025-06-06 Mengjiao Bai , Huaian Diao , Weisheng Zhou

We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous reference can be uniquely determined by (single-)scattered…

Analysis of PDEs · Mathematics 2026-05-01 Matti Lassas , Shiqi Ma , Lauri Oksanen , Mikko Salo , Jian Zhai

In this paper, we give a positive answer to a challenging open problem for recovering unknown obstacle (which is usually referred to as a scatterer) by acoustic wave probe associated to the Helmholtz equation. We show that the acoustic…

Analysis of PDEs · Mathematics 2021-04-20 Genqian Liu

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

Analysis of PDEs · Mathematics 2018-12-03 Heping Dong , Jun Lai , Peijun Li

Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions…

Analysis of PDEs · Mathematics 2018-01-17 Johannes Elschner , Guanghui Hu

Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…

Analysis of PDEs · Mathematics 2013-05-07 Jiaqing Yang , Bo Zhang

Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(\beta,\alpha_0,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely. Here $\alpha_0\in S^2$ is a fixed…

Mathematical Physics · Physics 2015-05-20 A. G. Ramm

We consider a polyhedron with zero classical resistance, i.e., a polyhedron invisible to an observer viewing only the paths of geometrical optics rays. The corresponding problem of scattering of plane waves by the polyhedron is studied. The…

Mathematical Physics · Physics 2012-04-19 E. Lakshtanov , B. D. Sleeman , B. Vainberg

In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability…

Analysis of PDEs · Mathematics 2022-02-24 Hongyu Liu , Chun-Hsiang Tsou

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

It was proved in \cite{NS1} that obstacles $K$ in $\R^d$ that are finite disjoint unions of strictly convex domains with $C^3$ boundaries are uniquely determined by the travelling times of billiard trajectories in their exteriors and also…

Dynamical Systems · Mathematics 2019-10-11 Lyle Noakes , Luchezar Stoyanov

We consider the scattering problem governed by the Helmholtz equation with inhomogeneity in both `conductivity' in the divergence form and `potential' in the lower order term. The support of the inhomogeneity is assumed to contain a convex…

Analysis of PDEs · Mathematics 2020-09-14 Fioralba Cakoni , Jingni Xiao

We develop two inverse scattering schemes for locating multiple electromagnetic (EM) scatterers by the electric far-field measurement corresponding to a single incident/detecting plane wave. The first scheme is for locating scatterers of…

Analysis of PDEs · Mathematics 2013-01-28 Jingzhi Li , Hongyu Liu , Zaijiu Shang , Hongpeng Sun

We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely the obstacle is restricted to a two-dimensional plane and interacting with a arbitrary incident wave, it scatters acoustic waves to…

Analysis of PDEs · Mathematics 2020-07-20 Emilia Blåsten , Lassi Päivärinta , Sadia Sadique

This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…

Analysis of PDEs · Mathematics 2026-04-14 Jialei Li , Xiaodong Liu

We consider the inverse obstacle scattering problem of determining both the shape and the "equivalent impedance" from far field measurements at a fixed frequency. In this work, the surface impedance is represented by a second order surface…

Numerical Analysis · Mathematics 2013-07-24 Laurent Bourgeois , Nicolas Chaulet , Houssem Haddar