Corpus ID: 236881076

Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunction

@inproceedings{Liu2021StableDB,
  title={Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunction},
  author={Hongyu Liu and Chun-Hsiang Tsou},
  year={2021}
}
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 result in determining a polygonal scatterer by a single far-field measurement. The argument in establishing the stability result is localised around a corner and can be as well used to produce two highly intriguing implications for invisibility and transmission… Expand

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References

SHOWING 1-10 OF 48 REFERENCES
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 anExpand
Scattering by Curvatures, Radiationless Sources, Transmission Eigenfunctions, and Inverse Scattering Problems
TLDR
It is shown that a scatterer cannot be completely invisible if its support is sufficiently small (compared to the underlying wavelength and scattering intensity), and new intrinsic geometric properties of interior transmission eigenfunctions near high-curvature points are derived. Expand
On vanishing near corners of conductive transmission eigenfunctions.
In this paper, we consider the transmission eigenvalue problem associated with a general conductive transmission condition and study the geometric structures of the transmission eigenfunctions. WeExpand
On corner scattering for operators of divergence form and applications to inverse scattering
Abstract 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 ofExpand
Shape Identification in Inverse Medium Scattering Problems with a Single Far-Field Pattern
TLDR
It is shown that the smoothness conditions in previous corner scattering results are only required near the corners, and it is proved that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. Expand
On vanishing and localizing of transmission eigenfunctions near singular points: a numerical study
This paper is concerned with the intrinsic geometric structure of interior transmission eigenfunctions arising in wave scattering theory. We numerically show that the aforementioned geometricExpand
On Electromagnetic Scattering from a Penetrable Corner
TLDR
It is shown that an EM medium, whose support has a right corner, scatters every pair of incident EM fields, excluding a possible class of EM fields which are of very particular forms. Expand
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 R N , N ≥ 2, by a minimal number of far-field measurements. This work isExpand
Recovering piecewise constant refractive indices by a single far-field pattern
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-fieldExpand
Acoustic Scattering from Corners, Edges and Circular Cones
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 edgeExpand
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