{
  "id": "1204.3938",
  "version": "v1",
  "published": "2012-04-17T23:12:11.000Z",
  "updated": "2012-04-17T23:12:11.000Z",
  "title": "An aggregation equation with degenerate diffusion: qualitative property of solutions",
  "authors": [
    "Lincoln Chayes",
    "Inwon Kim",
    "Yao Yao"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a nonlocal aggregation equation with degenerate diffusion, set in a periodic domain. This equation represents the generalization to $m > 1$ of the McKean-Vlasov equation where here the \"diffusive\" portion of the dynamics are governed by Porous medium self-interactions. We focus primarily on $m\\in(1,2]$ with particular emphasis on $m = 2$. In general, we establish regularity properties and, for small interaction, exponential decay to the uniform stationary solution. For $m=2$, we obtain essentially sharp results on the rate of decay for the entire regime up to the (sharp) transitional value of the interaction parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-17T23:12:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "degenerate diffusion",
      "qualitative property",
      "nonlocal aggregation equation",
      "uniform stationary solution",
      "equation represents"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.3938C"
    }
  }
}