{
  "id": "1107.2153",
  "version": "v2",
  "published": "2011-07-11T21:41:37.000Z",
  "updated": "2011-08-17T16:08:33.000Z",
  "title": "Total Variation Flow and Sign Fast Diffusion in one dimension",
  "authors": [
    "Matteo Bonforte",
    "Alessio Figalli"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the dynamics of the Total Variation Flow (TVF) $u_t=\\div(Du/|Du|)$ and of the Sign Fast Diffusion Equation (SFDE) $u_t=\\Delta\\sign(u)$ in one spatial dimension. We find the explicit dynamic and sharp asymptotic behaviour for the TVF, and we deduce the one for the SFDE by an explicit correspondence between the two equations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-17T16:08:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K59",
      "35K67",
      "35K92",
      "35B40"
    ],
    "keywords": [
      "total variation flow",
      "sign fast diffusion equation",
      "sharp asymptotic behaviour",
      "explicit correspondence",
      "spatial dimension"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2012.01.003",
      "journal": "Journal of Differential Equations",
      "year": 2012,
      "volume": 252,
      "number": 8,
      "pages": 4455
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JDE...252.4455B"
    }
  }
}