{
  "annotation_id": "a9d797ff-adca-4d25-be59-bf7f266fa452",
  "date_created": "2026-03-02T18:00:28.836000Z",
  "date_modified": "2026-03-02T18:00:28.836000Z",
  "file_hash": "0dc7719154c224c167eb4e11e1d69d3b27f8cdc4f179d7914450ccf54099387d",
  "private": false,
  "record": {
    "abstract": "We give an integral variational characterization for the speed of fronts of\nthe nonlinear diffusion equation $u_t = u_{xx} + f(u)$ with $f(0)=f(1)=0$, and\n$f\u003e0$ in $(0,1)$, which permits, in principle, the calculation of the exact\nspeed for arbitrary $f$.",
    "arxiv_id": "patt-sol/9408001",
    "authors": [
      "R. D. Benguria",
      "M. C. Depassier"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1007/BF02101631",
    "journal_ref": "Commun. Math. Phys., 175 (1996) 221",
    "title": "Variational Characterization of the Speed of Propagation of Fronts for   the Nonlinear Diffusion Equation",
    "url": "https://arxiv.org/abs/patt-sol/9408001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "de4a4daa-415d-4bec-b342-a2372d9ef83b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}