{
  "id": "2301.07847",
  "version": "v1",
  "published": "2023-01-19T02:00:55.000Z",
  "updated": "2023-01-19T02:00:55.000Z",
  "title": "Stability for Time-domain Elastic Wave Equations",
  "authors": [
    "Bochao Chen",
    "Yixian Gao",
    "Shuguan Ji",
    "Yang Liu"
  ],
  "comment": "23pp",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the Dirichlet-to-Neumann operator. The reconstruction is mainly based on the modified boundary control method and complex geometric optics solutions for the elastic wave. Next, the stable observability is obtained by a Carleman estimate. Finally, the stability for the density is presented by the connect operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-19T02:00:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time-domain elastic wave equations",
      "complex geometric optics solutions",
      "explicit reconstruction formula",
      "modified boundary control method",
      "dimensional domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}