{
  "id": "1205.4160",
  "version": "v1",
  "published": "2012-05-18T13:56:27.000Z",
  "updated": "2012-05-18T13:56:27.000Z",
  "title": "A weak comparison principle for reaction-diffusion systems",
  "authors": [
    "José Valero"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation and to a model of fractional-order chemical autocatalysis with decay. Morever, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions $L^{\\infty}$ is proved for at least one solution of the problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-18T13:56:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B09",
      "35B50",
      "35B51",
      "35K55",
      "35K57"
    ],
    "keywords": [
      "weak comparison principle",
      "reaction-diffusion system",
      "lotka-volterra system",
      "weak maximum principle",
      "generalized logistic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.4160V"
    }
  }
}