{
  "id": "0812.4977",
  "version": "v1",
  "published": "2008-12-29T21:45:10.000Z",
  "updated": "2008-12-29T21:45:10.000Z",
  "title": "Decay of mass for nonlinear equation with fractional Laplacian",
  "authors": [
    "Ahmad Fino",
    "Grzegorz Karch"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The large time behavior of nonnegative solutions to the reaction-diffusion equation $\\partial_t u=-(-\\Delta)^{\\alpha/2}u - u^p,$ $(\\alpha\\in(0,2], p>1)$ posed on $\\mathbb{R}^N$ and supplemented with an integrable initial condition is studied. We show that the anomalous diffusion term determines the large time asymptotics for $p>1+{\\alpha}/{N},$ while nonlinear effects win if $p\\leq1+{\\alpha}/{N}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-29T21:45:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35B40",
      "60H99"
    ],
    "keywords": [
      "fractional laplacian",
      "nonlinear equation",
      "nonlinear effects win",
      "anomalous diffusion term determines",
      "large time asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4977F"
    }
  }
}