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We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

Analysis of PDEs · Mathematics 2014-12-12 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella , Jian Zhai

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

In this work, we consider the time-harmonic inverse elastic source problem of a fixed frequency for the Navier equation in two dimensions. We show that a convex polygon can be uniquely determined by a single far field measurement. Our…

Analysis of PDEs · Mathematics 2025-06-04 Jianli Xiang

Consider the scattering of a time-harmonic elastic plane wave by a periodic rigid surface. The elastic wave propagation is governed by the two-dimensional Navier equation. Based on a Dirichlet-to-Neumann (DtN) map, a transparent boundary…

Numerical Analysis · Mathematics 2020-02-19 Peijun Li , Xiaokai Yuan

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the…

Mathematical Physics · Physics 2010-11-09 Evgeny Lakshtanov , Boris Vainberg

The inverse scattering problem for biharmonic waves, governing flexural vibrations of elastic plates, presents fundamental analytical challenges distinct from acoustic inverse problems due to the fourth-order differential operator and…

Numerical Analysis · Mathematics 2026-05-05 Tielei Zhu , Zhihao Ge , Bangmin Wu

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

We establish sharp stability estimates of logarithmic type in determining an impedance obstacle in $\mathbb{R}^2$. The obstacle is of general polygonal shape and the impedance parameter can be variable. We establish the stability results by…

Analysis of PDEs · Mathematics 2023-05-16 Huaian Diao , Hongyu Liu , Longyue Tao

In this paper a wave is generated by an initial data whose support is localized at the outside of unknown obstacles and observed in a limited time on a known closed surface or the same position as the support of the initial data. The…

Analysis of PDEs · Mathematics 2020-01-27 Masaru Ikehata

We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in…

Analysis of PDEs · Mathematics 2023-04-06 Pu-Zhao Kow , Yi-Hsuan Lin , Jenn-Nan Wang

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…

Analysis of PDEs · Mathematics 2015-05-18 Xiaodong Liu , Bo Zhang , Jiaqing Yang

The recovery of anomalies from backscattering far field data is a long-standing open problem in inverse scattering theory. We make a first step in this direction by establishing the unique identifiability of convex impenetrable obstacles…

Numerical Analysis · Mathematics 2025-12-29 Jialei Li , Xiaodong Liu , Qingxiang Shi

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

This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…

Analysis of PDEs · Mathematics 2009-12-09 xiaodong Liu , Bo Zhang

This work is concerned with an inverse electromagnetic scattering problem in two dimensions. We prove that in the TE polarization case, the knowledge of the electric far-field pattern incited by a single incoming wave is sufficient to…

Analysis of PDEs · Mathematics 2019-02-20 Guanghui Hu , Long Li , Jun Zou

Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a…

Analysis of PDEs · Mathematics 2012-11-19 Armin Lechleiter , Dinh-Liem Nguyen

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

An inverse obstacle scattering problem for the electromagnetic wave governed by the Maxwell system over a finite time interval is considered. It is assumed that the wave satisfies the Leontovich boundary condition on the surface of an…

Analysis of PDEs · Mathematics 2019-02-22 Masaru Ikehata

Consider the elastic scattering of an incident wave by a rigid obstacle in three dimensions, which is formulated as an exterior problem for the Navier equation. By constructing a Dirichlet-to-Neumann (DtN) operator and introducing a…

Numerical Analysis · Mathematics 2021-01-18 Gang Bao , Peijun Li , Xiaokai Yuan

We determine the uniqueness on starlike obstacles by using the cross section data. We see cross section data as spectral measure in polar coordinate at far field. Cross section scattering data suffice to give the local behavior of the wave…

Analysis of PDEs · Mathematics 2010-11-15 Lung-Hui Chen