{
  "id": "1609.01441",
  "version": "v1",
  "published": "2016-09-06T08:58:53.000Z",
  "updated": "2016-09-06T08:58:53.000Z",
  "title": "How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms?",
  "authors": [
    "Grégoire Nadin"
  ],
  "doi": "10.3934/dcdsb.2015.20.1785",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "We consider one-dimensional reaction-diffusion equations of Fisher-KPP type with random stationary ergodic coefficients. A classical result of Freidlin and Gartner [16] yields that the solutions of the initial value problems associated with compactly supported initial data admit a linear spreading speed almost surely. We use in this paper a new characterization of this spreading speed recently proved in [8] in order to investigate the dependence of this speed with respect to the heterogeneity of the diffusion and reaction terms. We prove in particular that adding a reaction term with null average or rescaling the coefficients by the change of variables x $\\rightarrow$ x/L, with L \\textgreater{} 1, speeds up the propagation. From a modelling point of view, these results mean that adding some heterogeneity in the medium gives a higher invasion speed, while fragmentation of the medium slows down the invasion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-06T08:58:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random stationary diffusion",
      "reaction term",
      "fisher-kpp equation",
      "random stationary ergodic coefficients",
      "initial value problems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}