{
  "id": "1103.1097",
  "version": "v1",
  "published": "2011-03-06T03:24:39.000Z",
  "updated": "2011-03-06T03:24:39.000Z",
  "title": "Recovery of a source term or a speed with one measurement and applications",
  "authors": [
    "Plamen Stefanov",
    "Gunther Uhlmann"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the problem of recovery the source $a(t,x)F(x)$ in the wave equation in anisotropic medium with $a$ known so that $a(0,x)\\not=0$ with a single measurement. We use Carleman estimates combined with geometric arguments and give sharp conditions for uniqueness. We also study the non-linear problem of recovery the sound speed in the equation $u_{tt} -c^2(x)\\Delta u =0$ with one measurement. We give sharp conditions for stability, as well. An application to thermoacoustic tomography is also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-06T03:24:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30"
    ],
    "keywords": [
      "source term",
      "application",
      "sharp conditions",
      "thermoacoustic tomography",
      "wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1097S"
    }
  }
}