{
  "id": "1709.02118",
  "version": "v1",
  "published": "2017-09-07T07:41:49.000Z",
  "updated": "2017-09-07T07:41:49.000Z",
  "title": "Detecting a hidden obstacle via the time domain enclosure method. A scalar wave case",
  "authors": [
    "Masaru Ikehata"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The characterization problem of the existence of an unknown obstacle behind a known obstacle is considered by using a singe observed wave at a place where the wave is generated. The unknown obstacle is invisible from the place by using visible ray. A mathematical formulation of the problem using the classical wave equation is given. The main result consists of two parts: (i) one can make a decision whether the unknown obstacle exists or not behind a known impenetrable obstacle by using a single wave over a finte time interval under some a-priori information on the position of the unknown obstacle; (ii) one can obtain a lower bound of the Euclidean distance of the unknown obstacle to the center point of the support of the intial data of the wave. The proof is a combination of the time domain enclosure method and some previous results on the Gaussian lower estimates for the heat kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-07T07:41:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35L05",
      "35K08"
    ],
    "keywords": [
      "time domain enclosure method",
      "scalar wave case",
      "unknown obstacle",
      "hidden obstacle",
      "gaussian lower estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}