{
  "id": "1510.08209",
  "version": "v1",
  "published": "2015-10-28T07:00:17.000Z",
  "updated": "2015-10-28T07:00:17.000Z",
  "title": "On finding an obstacle with the Leontovich boundary condition via the time domain enclosure method",
  "authors": [
    "Masaru Ikehata"
  ],
  "comment": "32pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "An inverse obstacle scattering problem for the wave governed by the Maxwell system in the time domain, in particular, over a finite time interval is considered. It is assumed that the electric field $\\mbox{\\boldmath $E$}$ and magnetic field $\\mbox{\\boldmath $H$}$ which are solutions of the Maxwell system are generated only by a current density at the initial time located not far a way from an unknown obstacle. The obstacle is embedded in a medium like air which has constant electric permittivity $\\epsilon$ and magnetic permeability $\\mu$. It is assumed that the fields on the surface of the obstacle satisfy the impedance-or the Leontovich boundary condition $\\mbox{\\boldmath $\\nu$}\\times\\mbox{\\boldmath $H$} -\\lambda\\,\\mbox{\\boldmath $\\nu$}\\times(\\mbox{\\boldmath $E$}\\times\\mbox{\\boldmath $\\nu$})=\\mbox{\\boldmath $0$}$ with $\\lambda$ an unknown positive function and $\\mbox{\\boldmath $\\nu$}$ the unit outward normal. The observation data are given by the electric field observed at the same place as the support of the current density over a finite time interval. It is shown that an indicator function computed from the electric fields corresponding two current densities enables us to know: the distance of the center of the common spherical support of the current densities to the obstacle; whether the value of the impedance $\\lambda$ is greater or less than the special value $\\sqrt{\\epsilon/\\mu}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-28T07:00:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35L50",
      "35Q61",
      "78A46",
      "78M35"
    ],
    "keywords": [
      "time domain enclosure method",
      "leontovich boundary condition",
      "current density",
      "finite time interval",
      "electric field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151008209I"
    }
  }
}