{
  "id": "1709.00923",
  "version": "v1",
  "published": "2017-09-04T12:35:47.000Z",
  "updated": "2017-09-04T12:35:47.000Z",
  "title": "Propagation in a Fisher-KPP equation with non-local advection *",
  "authors": [
    "François Hamel",
    "Christopher Henderson"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the influence of a general non-local advection term of the form K * u to propagation in the one-dimensional Fisher-KPP equation. This model is a generalization of the Keller-Segel-Fisher system. When K $\\in$ L 1 (R), we obtain explicit upper and lower bounds on the propagation speed which are asymptotically sharp and more precise than previous works. When K $\\in$ L p (R) with p > 1 and is non-increasing in (--$\\infty$, 0) and in (0, +$\\infty$), we show that the position of the \"front\" is of order O(t 1/p) if p < $\\infty$ and O(e $\\lambda$t) for some $\\lambda$ > 0 if p = $\\infty$ and K(+$\\infty$) > 0. We use a wide range of techniques in our proofs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-04T12:35:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "propagation",
      "general non-local advection term",
      "one-dimensional fisher-kpp equation",
      "keller-segel-fisher system",
      "explicit upper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}