{
  "id": "1206.6089",
  "version": "v1",
  "published": "2012-06-26T19:20:02.000Z",
  "updated": "2012-06-26T19:20:02.000Z",
  "title": "Increasing powers in a degenerate parabolic logistic equation",
  "authors": [
    "José Francisco Rodrigues",
    "Hugo Tavares"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$ \\partial_t u-\\Delta u=a u-b(x) u^p \\text{in} \\Omega\\times \\R^+, u(0)=u_0, u(t)|_{\\partial \\Omega}=0 $$ as $p\\to +\\infty$, where $\\Omega$ is a bounded domain and $b(x)$ is a nonnegative function. We deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards we fully describe its long time behavior.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-26T19:20:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B09",
      "35K91"
    ],
    "keywords": [
      "degenerate parabolic logistic equation",
      "increasing powers",
      "long time behavior",
      "parabolic obstacle problem",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.6089F"
    }
  }
}