{
  "annotation_id": "dd0e6985-e1d2-43f5-95d2-997894e4db58",
  "date_created": "2026-03-02T18:00:28.597000Z",
  "date_modified": "2026-03-02T18:00:28.597000Z",
  "file_hash": "e2d5239c51eac7af7150c7eb1aeb7b350eb6bdca4f847408df2aa22eadc6eb97",
  "private": false,
  "record": {
    "abstract": "We study the speed of propagation of fronts for the scalar reaction-diffusion\nequation $u_t = u_{xx} + f(u)$\\, with $f(0) = f(1) = 0$. We give a new integral\nvariational principle for the speed of the fronts joining the state $u=1$ to\n$u=0$. No assumptions are made on the reaction term $f(u)$ other than those\nneeded to guarantee the existence of the front. Therefore our results apply to\nthe classical case $f \u003e 0$ in $(0,1)$, to the bistable case and to cases in\nwhich $f$ has more than one internal zero in $(0,1)$.",
    "arxiv_id": "patt-sol/9511003",
    "authors": [
      "R. D. Benguria",
      "M. C. Depassier"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevLett.77.1171",
    "journal_ref": "Phys. Rev. Lett., 77 (1996) 1171",
    "title": "The Speed of Fronts of the Reaction Diffusion Equation",
    "url": "https://arxiv.org/abs/patt-sol/9511003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0dae20f4-8bfe-44e4-ba65-c8ab8e46c3d4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}