{
  "id": "1708.07542",
  "version": "v1",
  "published": "2017-08-24T20:20:54.000Z",
  "updated": "2017-08-24T20:20:54.000Z",
  "title": "Smoothness and long time existence for solutions of the porous medium equation on manifolds with conical singularities",
  "authors": [
    "Nikolaos Roidos",
    "Elmar Schrohe"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the porous medium equation on manifolds with conical singularities. Given strictly positive initial values, we show that the solution exists in the maximal $L^{q}$-regularity space for all times and is instantaneously smooth in space and time, where the maximal $L^{q}$-regularity is obtained in the sense of Mellin-Sobolev spaces. Moreover, we obtain precise information concerning the asymptotic behavior of the solution close to the singularity. Finally, we show the existence of generalized solutions for non-negative initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-24T20:20:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K59",
      "35K65",
      "35R01"
    ],
    "keywords": [
      "porous medium equation",
      "long time existence",
      "singularity",
      "conical singularities",
      "smoothness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}