{
  "id": "1010.4285",
  "version": "v1",
  "published": "2010-10-20T19:21:52.000Z",
  "updated": "2010-10-20T19:21:52.000Z",
  "title": "Viscosity Solutions for the two-phase Stefan Problem",
  "authors": [
    "Inwon C. Kim",
    "Norbert Pozar"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We introduce a notion of viscosity solutions for the two-phase Stefan problem, which incorporates possible existence of a mushy region generated by the initial data. We show that a comparison principle holds between viscosity solutions, and investigate the coincidence of the viscosity solutions and the weak solutions defined via integration by parts. In particular, in the absence of initial mushy region, viscosity solution is the unique weak solution with the same boundary data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-20T19:21:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35",
      "80A22",
      "35B51",
      "35D40"
    ],
    "keywords": [
      "viscosity solution",
      "two-phase stefan problem",
      "comparison principle holds",
      "initial mushy region",
      "unique weak solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4285K"
    }
  }
}