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We propose an inverse scattering scheme of recovering a polyhedral obstacle in $\mathbb{R}^n$, $n=2,3$, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the…

Analysis of PDEs · Mathematics 2015-02-05 Jingzhi Li , Hongyu Liu

The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz hypersurface. They…

Analysis of PDEs · Mathematics 2020-10-28 Pedro Caro , Andoni Garcia

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

Analysis of PDEs · Mathematics 2014-12-17 Aníbal Coronel , Marko Rojas-Medar

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schr\"odinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first…

Analysis of PDEs · Mathematics 2020-04-29 Jingzhi Li , Hongyu Liu , Shiqi Ma

This paper is concerned with the inverse elastic scattering problem to determine the shape and location of an elastic cavity. By establishing a one-to-one correspondence between the Herglotz wave function and its kernel, we introduce the…

Numerical Analysis · Mathematics 2024-09-17 Shuxin Li , Junliang Lv , Yi Wang

This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…

Numerical Analysis · Mathematics 2023-07-05 Youzi He , Hongyu Liu , Xianchao Wang

In this paper, we study the direct and inverse scattering of the Schr\"odinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the…

Analysis of PDEs · Mathematics 2024-02-27 Yan Chang , Yukun Guo , Yue Zhao

Problem for a cubic string having the shape of a step is studied. It is proved that here we have two scattering problems: the direct one and its dual. The direct problem describes scattering of the waves coming from ``$+\infty$'', and its…

Classical Analysis and ODEs · Mathematics 2025-09-09 Vladimir A. Zolotarev

We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…

Analysis of PDEs · Mathematics 2017-05-24 Hongyu Liu , Xiaodong Liu

Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…

Analysis of PDEs · Mathematics 2019-04-18 Yang Liu , Yixian Gao , Jian Zu

We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by…

Analysis of PDEs · Mathematics 2023-04-25 Shiqi Ma , Leyter Potenciano-Machado , Mikko Salo

We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we…

Mathematical Physics · Physics 2015-02-17 Roman Novikov

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

This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…

Analysis of PDEs · Mathematics 2018-12-26 Alexey Agaltsov , Thorsten Hohage , Roman Novikov

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

Exceptional points (EPs) in non-Hermitian photonic systems enable unconventional control of wave amplitude and phase. However, identifying the EPs in multidimensional parameter space of a system can be nontrivial and, in some cases, even…

Optics · Physics 2026-04-17 Y. F. Li , Biao Chen , Y. Wu , Y. Liu , H. Lin , Bin Zhou

This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer…

Numerical Analysis · Mathematics 2024-12-20 Xiaoli Liu , Ruming Zhang

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

Numerical Analysis · Mathematics 2025-01-22 Carlos Castro , Sorin Micu

The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…

Mathematical Physics · Physics 2011-11-28 Tamas Palmai , Barnabas Apagyi