Unique determination by a single far-field measurement for an inverse elastic problem
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.
Keywords
Cite
@article{arxiv.2311.16435,
title = {Unique determination by a single far-field measurement for an inverse elastic problem},
author = {Huaian Diao and Ruixiang Tang and Hongyu Liu and Jiexin Tang},
journal= {arXiv preprint arXiv:2311.16435},
year = {2023}
}