"通过单次远场测量确定声软多面体散射体“的勘误表

用单次远场测量确定声软多面体散射体

Determining a sound-soft polyhedral scatterer by a single far-field measurement

我们证明了一个软声多面体散射体是唯一确定的远场图案对应于入射平面波在一个给定的波数和一个给定的入射方向。

Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements

The aim of the paper is to establish optimal stability estimates for the determination of sound-hard polyhedral scatterers in $\mathbb{R}^N$, $N \geq 2$, by a minimal number of far-field measurements. This work is a significant and highly nontrivial extension of the stability estimates for the determination of sound-soft polyhedral scatterers by far-field measurements, proved by one of the authors, to the much more challenging sound-hard case. The admissible polyhedral scatterers satisfy minimal a priori assumptions of Lipschitz type and may include at the same time solid obstacles and screen-…

Inverse time-harmonic electromagnetic scattering from coated polyhedral scatterers with a single far-field pattern

It is proved that a convex polyhedral scatterer of impedance type can be uniquely determined by the electric far-field pattern of a non-vanishing incident field. The incoming wave is allowed to bean electromagnetic plane wave, a vector Herglotz wave function or a point source wave incited by some magnetic dipole. Our proof relies on the reflection principle for Maxwell's equations with the impedance (or Leontovich) boundary condition enforcing on a hyper-plane. We prove that it is impossible to analytically extend the total field across any vertex of the scatterer. This leads to a data-driven …

Stable determination of an elastic medium scatterer by a single far-field measurement and beyond

We are concerned with the time-harmonic elastic scattering due to an inhomogeneous elastic material inclusion located inside a uniformly homogeneous isotropic medium. We establish a sharp stability estimate of logarithmic type in determining the support of the elastic scatterer, independent of its material content, by a single far-field measurement when the support is a convex polyhedral domain in $\mathbb{R}^n$, $n=2,3$. Our argument in establishing the stability result is localized around a corner of the medium scatterer. This enables us to further establish a byproduct result by proving tha…

弹性波解耦及其应用

Decoupling Elastic Waves and Its Applications

本文研究了由Lamé系统控制的时谐弹性波散射问题。众所周知，弹性波场可以分解为剪切波和压缩波部分，即通常共存但以不同速度传播的压力波和剪切波。考虑第三类和第四类散射体，分别导出了与散射体边界面的平均曲率和高斯曲率有关的两个几何条件，保证了剪切波和压力波的解耦。然后，我们应用解耦结果的唯一性和稳定性分析的逆弹性散射问题确定多面体散射体的最小数量的远场测量。

On corners scattering stably and stable shape determination by a single far-field pattern

In this paper, we establish two sharp quantitative results for the direct and inverse time-harmonic acoustic wave scattering. The first one is concerned with the recovery of the support of an inhomogeneous medium, independent of its contents, by a single far-field measurement. For this challenging inverse scattering problem, we establish a sharp stability estimate of logarithmic type when the medium support is a polyhedral domain in $\mathbb{R}^n$, $n=2,3$. The second one is concerned with the stability for corner scattering. More precisely if an inhomogeneous scatterer, whose support has a co…