{
  "id": "1909.03711",
  "version": "v1",
  "published": "2019-09-09T09:17:57.000Z",
  "updated": "2019-09-09T09:17:57.000Z",
  "title": "Semi-wave and spreading speed of the nonlocal Fisher-KPP equation with free boundaries",
  "authors": [
    "Yihong Du",
    "Fang Li",
    "Maolin Zhou"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "In Cao, Du, Li and Li [8], a nonlocal diffusion model with free boundaries extending the local diffusion model of Du and Lin [12] was introduced and studied. For Fisher-KPP type nonlinearities, its long-time dynamical behaviour is shown to follow a spreading-vanishing dichotomy. However, when spreading happens, the question of spreading speed was left open in [8]. In this paper we obtain a rather complete answer to this question. We find a condition on the kernel function such that spreading grows linearly in time exactly when this condition holds, which is achieved by completely solving the associated semi-wave problem that determines this linear speed; when the kernel function violates this condition, we show that accelerating spreading happens.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-09T09:17:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K57",
      "35R20",
      "92D25"
    ],
    "keywords": [
      "nonlocal fisher-kpp equation",
      "free boundaries",
      "fisher-kpp type nonlinearities",
      "spreading happens",
      "kernel function violates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}