{
  "id": "math/0611218",
  "version": "v1",
  "published": "2006-11-08T09:29:50.000Z",
  "updated": "2006-11-08T09:29:50.000Z",
  "title": "Two sides of probe method and obstacle with impedance boundary condition",
  "authors": [
    "Masaru Ikehata"
  ],
  "comment": "19pages",
  "journal": "Hokkaido Math. J., 35(2006), 659-681",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin condition) from the associated Dirichlet-to-Neumann map. The main result is a characterization of the unknown obstacle via the sequences that are constructed by the Dirichlet-to-Neumann map, under smallness conditions on the wave number and the upper bound of the impedance. Moreover two alternative simple proofs of a previous result of Cheng-Liu-Nakamura which are based on only some energy estimates, an analysis of the blowup of the energy of so-called reflected solutions and an application of the enclosure method to the problem are also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-08T09:29:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30"
    ],
    "keywords": [
      "probe method",
      "dirichlet-to-neumann map",
      "inverse boundary value problem",
      "unknown impedance boundary condition",
      "unknown obstacle"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11218I"
    }
  }
}