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This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique and the superpositions of two point sources as the incident…

Analysis of PDEs · Mathematics 2020-02-19 Deyue Zhang , Yinglin Wang , Yukun Guo , Jingzhi Li

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

In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…

Analysis of PDEs · Mathematics 2020-12-10 Fang Zeng , Shixu Meng

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 consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain $\Omega\subset\mathbb{R}^N$ ($N\geq 2$). {In a subregion $D\Subset\Omega$, the medium is supposed to be lossy and have a large…

Analysis of PDEs · Mathematics 2015-06-03 Hongyu Liu , Zaijiu Shang , Hongpeng Sun , Jun Zou

In this paper, we consider the obstacle scattering problem for biharmonic equations with a Dirichlet boundary condition in both two and three dimensions. Some basic properties are first derived for the biharmonic scattering solutions, which…

Analysis of PDEs · Mathematics 2025-10-16 Chengyu Wu , Jiaqing Yang

It is proved that the scattering amplitude $A(\beta, \alpha_0, k_0)$, known for all $\beta\in S^2$, where $S^2$ is the unit sphere in $\mathbb{R}^3$, and fixed $\alpha_0\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the…

Mathematical Physics · Physics 2017-05-30 A. G. Ramm

We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…

Analysis of PDEs · Mathematics 2024-10-31 Safiere Kuijpers , Laura Scarabosio

This paper considers 3-D elastic scattering problems by penetrable obstacles with embedded objects. The well-posedness of transmission problem is proved by employing integral equation method. Then the Inverse Problems , which is to recover…

Analysis of PDEs · Mathematics 2025-12-04 Chun Liu , Jiaqing Yang , Bo Zhang

It is proved that the scattering amplitude $A(\beta, \alpha_0, k_0)$, known for all $\beta\in S^2$, where $S^2$ is the unit sphere in $\mathbb{R}^3$, and fixed $\alpha_0\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the…

Numerical Analysis · Mathematics 2017-06-15 A. G. Ramm

In this work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal…

Analysis of PDEs · Mathematics 2021-04-27 Ibtissem Ben Aïcha , Guanghui Hu , Manmohan Vashisth , Jun Zou

We prove that a sound-soft polyhedral scatterer is uniquely determined by the far-field pattern corresponding to an incident plane wave at one given wavenumber and one given incident direction.

Analysis of PDEs · Mathematics 2007-05-23 Giovanni Alessandrini , Luca Rondi

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

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

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 consider the scattering of waves by a penetrable inclusion embedded in some reference medium. We exhibit examples of materials and geometries for which non-scattering frequencies exist, i.e., for which at some frequencies there are…

Analysis of PDEs · Mathematics 2024-12-20 Lucas Chesnel , Houssem Haddar , Hongjie Li , Jingni Xiao

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

We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the…

Analysis of PDEs · Mathematics 2022-02-14 Roland Griesmaier , Marvin Knöller , Rainer Mandel

This paper is concerned with inverse crack scattering problems for time-harmonic acoustic waves. We prove that a piecewise linear crack with the sound-soft boundary condition in two dimensions can be uniquely determined by the far-field…

Numerical Analysis · Mathematics 2024-05-09 Xiaoxu Xu , Guanqiu Ma , Guanghui Hu

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge