{
  "annotation_id": "d46f7a97-d712-4428-956a-41e0c3bf46bc",
  "date_created": "2026-03-02T18:00:28.849000Z",
  "date_modified": "2026-03-02T18:00:28.849000Z",
  "file_hash": "fcc3752b0548fe53b76613902c7899a64e7f225ddfc99e97e666541532446ecc",
  "private": false,
  "record": {
    "abstract": "We consider the problem of the speed selection mechanism for the one\ndimensional nonlinear diffusion equation $u_t = u_{xx} + f(u)$. It has been\nrigorously shown by Aronson and Weinberger that for a wide class of functions\n$f$, sufficiently localized initial conditions evolve in time into a monotonic\nfront which propagates with speed $c^*$ such that $2 \\sqrt{f\u0027(0)} \\leq c^* \u003c 2\n\\sqrt{\\sup(f(u)/u)}$. The lower value $c_L = 2 \\sqrt{f\u0027(0)}$ is that predicted\nby the linear marginal stability speed selection mechanism. We derive a new\nlower bound on the the speed of the selected front, this bound depends on $f$\nand thus enables us to assess the extent to which the linear marginal selection\nmechanism is valid.",
    "arxiv_id": "patt-sol/9403001",
    "authors": [
      "R. D. Benguria",
      "M. C. Depassier"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevLett.73.2272",
    "journal_ref": "Phys. Rev. Lett., 73 (1994) 2272",
    "title": "On the validity of the linear speed selection mechanism for fronts of   the nonlinear diffusion equation",
    "url": "https://arxiv.org/abs/patt-sol/9403001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fb55d00e-0b1c-4eeb-a8a1-57e75d6367a4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}