{
  "id": "2311.16435",
  "version": "v1",
  "published": "2023-11-28T02:31:54.000Z",
  "updated": "2023-11-28T02:31:54.000Z",
  "title": "Unique determination by a single far-field measurement for an inverse elastic problem",
  "authors": [
    "Huaian Diao",
    "Ruixiang Tang",
    "Hongyu Liu",
    "Jiexin Tang"
  ],
  "categories": [
    "math.AP"
  ],
  "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 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 polygonal-nest or polygonal-cell structure scatterers 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-28T02:31:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "74J20",
      "86A22"
    ],
    "keywords": [
      "single far-field measurement",
      "inverse elastic problem",
      "unique determination",
      "inverse elastic medium scattering problem",
      "polygonal-cell structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}