{
  "id": "2208.01306",
  "version": "v1",
  "published": "2022-08-02T08:25:45.000Z",
  "updated": "2022-08-02T08:25:45.000Z",
  "title": "Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation",
  "authors": [
    "Tatsu-Hiko Miura"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Neumann type problem of the heat equation in a moving thin domain around a given closed moving hypersurface. The main result of this paper is an error estimate in the sup-norm for classical solutions to the thin domain problem and a limit equation on the moving hypersurface which appears in the thin-film limit of the heat equation. To prove the error estimate, we show a uniform a priori estimate for a classical solution to the thin domain problem based on the maximum principle. Moreover, we construct a suitable approximate solution to the thin domain problem from a classical solution to the limit equation based on an asymptotic expansion of the thin domain problem and apply the uniform a priori estimate to the difference of the approximate solution and a classical solution to the thin domain problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-02T08:25:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K05",
      "35B25",
      "35R01",
      "35R37"
    ],
    "keywords": [
      "classical solution",
      "thin domain problem",
      "moving thin domain",
      "error estimate",
      "limit equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}