{
  "id": "1305.4888",
  "version": "v1",
  "published": "2013-05-21T17:15:11.000Z",
  "updated": "2013-05-21T17:15:11.000Z",
  "title": "Stability of the determination of a coefficient for the wave equation in an infinite wave guide",
  "authors": [
    "Yavar Kian"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the stability in the inverse problem consisting in the determination of an electric potential $q$, appearing in a Dirichlet initial-boundary value problem for the wave equation $\\partial_t^2u-\\Delta u+q(x)u=0$ in an unbounded wave guide $\\Omega=\\omega\\times\\mathbb R$ with $\\omega$ a bounded smooth domain of $\\mathbb R^2$, from boundary observations. The observation is given by the Dirichlet to Neumann map associated to a wave equation. We prove a H\\\"older stability estimate in the determination of $q$ from the Dirichlet to Neumann map. Moreover, provided that the gap between two electric potentials rich its maximum in a fixed bounded subset of $\\bar{\\Omega}$, we extend this result to the same inverse problem with measurements on a bounded subset of the lateral boundary $(0,T)\\times\\partial\\Omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-21T17:15:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35L20"
    ],
    "keywords": [
      "wave equation",
      "infinite wave guide",
      "determination",
      "coefficient",
      "neumann map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.4888K"
    }
  }
}