{
  "id": "2105.14518",
  "version": "v1",
  "published": "2021-05-30T12:35:50.000Z",
  "updated": "2021-05-30T12:35:50.000Z",
  "title": "Identification of source terms in heat equation with dynamic boundary conditions",
  "authors": [
    "E. M. Ait Ben Hassi",
    "S. E. Chorfi",
    "L. Maniar"
  ],
  "comment": "18 pages, 4 figures",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "We study an inverse parabolic problem of identifying two source terms in heat equation with dynamic boundary conditions from a final time overdetermination data. Using a weak solution approach by Hasanov, the associated cost functional is analyzed, especially a gradient formula of the functional is proved and given in terms of the solution of an adjoint problem. Next, the existence and uniqueness of a quasi-solution are also investigated. Finally, the numerical reconstruction of some heat sources in a 1-D equation is presented to show the efficiency of the proposed algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-30T12:35:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35K05",
      "49N45",
      "47A05"
    ],
    "keywords": [
      "dynamic boundary conditions",
      "heat equation",
      "source terms",
      "identification",
      "final time overdetermination data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}