{
  "id": "1004.1735",
  "version": "v1",
  "published": "2010-04-10T19:07:18.000Z",
  "updated": "2010-04-10T19:07:18.000Z",
  "title": "Sharp interface limit of the Fisher-KPP equation when initial data have slow exponential decay",
  "authors": [
    "Matthieu Alfaro",
    "Arnaud Ducrot"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the singular limit, as $\\ep \\to 0$, of the Fisher equation $\\partial_t u=\\ep \\Delta u + \\ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support plus perturbations with {\\it slow exponential decay}. We prove that the sharp interface limit moves by a constant speed, which dramatically depends on the tails of the initial data. By performing a fine analysis of both the generation and motion of interface, we provide a new estimate of the thickness of the transition layers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-10T19:07:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "slow exponential decay",
      "initial data",
      "fisher-kpp equation",
      "sharp interface limit moves",
      "compact support plus perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1735A"
    }
  }
}