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

Zhengjian Bai; Huaian Diao; Hongyu Liu; Qingle Meng

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arXiv · 2111.12288

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

Zhengjian Bai·Huaian Diao·Hongyu Liu·Qingle Meng

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Abstract

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 that if a generic medium scatterer, not necessary to be a polyhedral shape, possesses a corner, then there exists a positive lower bound of the scattered far-field patterns. The latter result indicates that if an elastic material object possesses a corner on its support, then it scatters every incident wave stably and invisibility phenomenon does not occur.

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Zhengjian Bai, Huaian Diao, Hongyu Liu, Qingle Meng. 2021-11-24. Stable determination of an elastic medium scatterer by a single far-field measurement and beyond. https://arxiv.org/abs/2111.12288

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