{
  "id": "2012.00611",
  "version": "v1",
  "published": "2020-11-30T10:46:11.000Z",
  "updated": "2020-11-30T10:46:11.000Z",
  "title": "On inverse problems modeled by PDE's",
  "authors": [
    "A. Leitao"
  ],
  "comment": "13 pages 5 figures. arXiv admin note: substantial text overlap with arXiv:2011.14441",
  "journal": "Matem\\'atica Contempor\\^anea 18 (2000), 195-207",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We investigate the iterative methods proposed by Maz'ya and Kozlov (see [3], [4]) for solving ill-posed reconstruction problems modeled by PDE's. We consider linear time dependent problems of elliptic, hyperbolic and parabolic types. Each iteration of the analyzed methods consists on the solution of a well posed boundary (or initial) value problem. The iterations are described as powers of affine operators, as in [4]. We give alternative convergence proofs for the algorithms, using spectral theory and some functional analytical results (see [5], [6]).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-30T10:46:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65J20",
      "47A52"
    ],
    "keywords": [
      "inverse problems",
      "linear time dependent problems",
      "solving ill-posed reconstruction problems",
      "parabolic types",
      "analyzed methods consists"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}