{
  "id": "1406.5734",
  "version": "v3",
  "published": "2014-06-22T15:19:26.000Z",
  "updated": "2015-06-02T23:06:38.000Z",
  "title": "Stability in the determination of a time-dependent coefficient for wave equations from partial data",
  "authors": [
    "Yavar Kian"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\\partial_t^2u-\\Delta u+q(t,x)u=0$ in $Q=(0,T)\\times\\Omega$ with $\\Omega$ a $C^2$ bounded domain of $\\mathbb R^n$, $n\\geq2$, from partial observations on $\\partial Q$. The observation is given by a boundary operator associated to the wave equation. Using suitable complex geometric optics solutions and Carleman estimates, we prove a stability estimate in the determination of $q$ from the boundary operator.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-17T08:55:58.000Z",
      "title": "Determination of a time-dependent coefficient for wave equations from partial data",
      "abstract": "We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\\partial_t^2u-\\Delta u+q(t,x)u=0$ in $Q=(0,T)\\times\\Omega$ with $\\Omega$ a bounded $C^2$ domain of $\\mathbb R^n$, $n\\geq3$, from partial observations on $\\partial Q$. The observation is given by a boundary operator associated to the wave equation. Using suitable complex geometric optics solutions and a Carleman estimate with linear weight, we prove a stability estimate in the determination of $q$ from the boundary operator.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-06-02T23:06:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35L05"
    ],
    "keywords": [
      "wave equation",
      "time-dependent coefficient",
      "partial data",
      "determination",
      "dirichlet initial-boundary value problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.5734K"
    }
  }
}