{
  "id": "1905.12232",
  "version": "v1",
  "published": "2019-05-29T06:09:54.000Z",
  "updated": "2019-05-29T06:09:54.000Z",
  "title": "Recovery of multiple coefficients in a reaction-diffusion equation",
  "authors": [
    "Barbara Kaltenbacher",
    "William Rundell"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the potential $q(x)$ in a parabolic equation from overposed data consisting of the value of solution profiles taken at a later time $T$. We show both uniqueness results and the convergence of an iteration scheme designed to recover these coefficients. We also allow a more general setting, in particular when the usual time derivative is replaced by one of fractional order and when the potential term is coupled with a known nonlinearity $f$ of the form $q(x)f(u)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-29T06:09:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "65M32",
      "35R11"
    ],
    "keywords": [
      "multiple coefficients",
      "reaction-diffusion equation",
      "solution profiles taken",
      "inverse problem",
      "parabolic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}