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arXiv · 2311.16435

Unique determination by a single far-field measurement for an inverse elastic problem

Huaian Diao·Ruixiang Tang·Hongyu Liu·Jiexin Tang
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Abstract

This paper is concerned with the unique identification of the shape of a scatterer through a single far-field pattern in an inverse elastic medium scattering problem with a generalized transmission boundary condition. The uniqueness issue by a single far-field measurement is a challenging problem in inverse scattering theory, which has a long and colorful history. In this paper, we demonstrate the well-posedness of the direct problem by the variational approach. We establish the uniqueness results by a single far-field measurement under a generic scenario when dealing with underlying elastic scatterers exhibiting polygonal-nest or polygonal-cell structures. Furthermore, for a polygonal-nest or polygonal-cell structure scatterer associated with density and boundary impedance parameters as piecewise constants, we show that these physical quantities can be uniquely determined simultaneously by a single far-field measurement. The corresponding proof relies heavily on examining the singular behaviour of a coupled PDE system near a corner in a microlocal manner.

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Huaian Diao, Ruixiang Tang, Hongyu Liu, Jiexin Tang. 2023-11-28. Unique determination by a single far-field measurement for an inverse elastic problem. https://arxiv.org/abs/2311.16435

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