{
  "id": "1204.5293",
  "version": "v2",
  "published": "2012-04-24T08:00:43.000Z",
  "updated": "2013-03-19T16:06:10.000Z",
  "title": "Stability of solutions to aggregation equation in bounded domains",
  "authors": [
    "Rafał Celiński"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the aggregation equation $u_t= \\div(\\nabla u-u\\nabla \\K(u))$ in a bounded domain $\\Omega\\subset \\R^d$ with supplemented the Neumann boundary condition and with a nonnegative, integrable initial datum. Here, $\\K=\\K(u)$ is an integral operator. We study the local and global existence of solutions and we derive conditions which lead us to either the stability or instability of constant solutions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-19T16:06:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35B40"
    ],
    "keywords": [
      "aggregation equation",
      "bounded domain",
      "neumann boundary condition",
      "constant solutions",
      "integral operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.5293C"
    }
  }
}