{
  "id": "1212.1422",
  "version": "v4",
  "published": "2012-12-06T19:16:50.000Z",
  "updated": "2013-10-20T09:17:33.000Z",
  "title": "Global stability and decay for the classical Stefan problem",
  "authors": [
    "Mahir Hadžić",
    "Steve Shkoller"
  ],
  "comment": "50 pages, references added, minor typos corrected, to appear in Comm. Pure Appl. Math, abstract added for UK REF",
  "categories": [
    "math.AP"
  ],
  "abstract": "The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free-boundary. We establish a global-in-time stability result for nearly spherical geometries and small temperatures, using a novel hybrid methodology, which combines energy estimates, decay estimates, and Hopf-type inequalities.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-10-20T09:17:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35",
      "35B65",
      "35K05",
      "80A22"
    ],
    "keywords": [
      "classical stefan problem",
      "global stability",
      "novel hybrid methodology",
      "priori unknown free-boundary",
      "global-in-time stability result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}