{
  "annotation_id": "00da2686-2a26-447f-8268-029bad068c77",
  "date_created": "2026-02-17T05:53:19.901000Z",
  "date_modified": "2026-02-17T05:53:19.901000Z",
  "file_hash": "9c22529cddf7f89a11043669b3bcb584a062b363df5339a2ed7e5881af5b35da",
  "private": false,
  "record": {
    "abstract": "We consider the parabolic $p$-Laplace equation with $p\u003e2$ in a moving thin domain under a Neumann type boundary condition corresponding to the total mass conservation. When the moving thin domain shrinks to a given closed moving hypersurface as its thickness tends to zero, we rigorously derive a limit problem by showing the weak convergence of the weighted average of a weak solution to the thin-domain problem and characterizing the limit function as a unique weak solution to the limit problem. The limit problem obtained in this paper is a system of a nonlinear partial differential equation and an algebraic equation on the moving hypersurface. This seems to be somewhat strange, but we also find that the limit problem can be seen as a new kind of local mass conservation law on the moving hypersurface with a normal flux.",
    "arxiv_id": "2601.09386",
    "authors": [
      "Tatsu-Hiko Miura"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Thin-film limit of the parabolic $p$-Laplace equation in a moving thin domain",
    "url": "https://arxiv.org/abs/2601.09386",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "828d9fe6-e63b-4f1d-9d46-25928b1f3c79",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}