{
  "id": "2102.07608",
  "version": "v1",
  "published": "2021-02-15T15:52:05.000Z",
  "updated": "2021-02-15T15:52:05.000Z",
  "title": "On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements",
  "authors": [
    "Barbara Kaltenbacher",
    "William Rundell"
  ],
  "journal": "Inverse Problems and Imaging, 2021",
  "doi": "10.3934/ipi.2021020",
  "categories": [
    "math.AP",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "We consider an undetermined coefficient inverse problem for a non-\\\\linear partial differential equation occurring in high intensity ultrasound propagation as used in acoustic tomography. In particular, we investigate the recovery of the nonlinearity coefficient commonly labeled as $B/A$ in the literature which is part of a space dependent coefficient $\\kappa$ in the Westervelt equation governing nonlinear acoustics. Corresponding to the typical measurement setup, the overposed data consists of time trace measurements on some zero or one dimensional set $\\Sigma$ representing the receiving transducer array. After an analysis of the map from $\\kappa$ to the overposed data, we show injectivity of its linearisation and use this as motivation for several iterative schemes to recover $\\kappa$. Numerical simulations will also be shown to illustrate the efficiency of the methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-15T15:52:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35K58",
      "35L72",
      "78A46"
    ],
    "keywords": [
      "boundary measurements",
      "nonlinearity parameter",
      "identification",
      "westervelt equation governing nonlinear acoustics",
      "high intensity ultrasound propagation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}