{
  "annotation_id": "536f6a8e-46c0-4abe-ad94-d147cacce4f6",
  "date_created": "2026-03-02T18:00:28.846000Z",
  "date_modified": "2026-03-02T18:00:28.846000Z",
  "file_hash": "c4d874a53051c55b042b16b17f152470122a144300bb05aa4dec3314640cb509",
  "private": false,
  "record": {
    "abstract": "We consider a nonlinear damped hyperbolic equation in $\\real^n$, $1 \\le n \\le\n4$, depending on a positive parameter $\\epsilon$. If we set $\\epsilon=0$, this\nequation reduces to the well-known Kolmogorov-Petrovski-Piskunov equation. We\nremark that, after a change of variables, this hyperbolic equation has the same\nfamily of one-dimensional travelling waves as the KPP equation. Using various\nenergy functionals, we show that, if $\\epsilon \u003e0$, these fronts are locally\nstable under perturbations in appropriate weighted Sobolev spaces. Moreover,\nthe decay rate in time of the perturbed solutions towards the front of minimal\nspeed $c=2$ is shown to be polynomial. In the one-dimensional case, if\n$\\epsilon \u003c 1/4$, we can apply a Maximum Principle for hyperbolic equations and\nprove a global stability result. We also prove that the decay rate of the\nperturbated solutions towards the fronts is polynomial, for all $c \u003e 2$.",
    "arxiv_id": "patt-sol/9602004",
    "authors": [
      "Th. Gallay",
      "G. Raugel"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1007/s000330050043",
    "title": "Stability of Travelling Waves for a Damped Hyperbolic Equation",
    "url": "https://arxiv.org/abs/patt-sol/9602004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f500e9b5-1536-4498-aff4-bcea25bc4d60",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}