{
  "id": "1607.00681",
  "version": "v1",
  "published": "2016-07-03T20:55:13.000Z",
  "updated": "2016-07-03T20:55:13.000Z",
  "title": "Local well-posedness and Global stability of the Two-Phase Stefan problem",
  "authors": [
    "Mahir Hadzic",
    "Gustavo Navarro",
    "Steve Shkoller"
  ],
  "comment": "58 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "The two-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, composed of two regions separated by an a priori unknown moving boundary which is transported by the difference (or jump) of the normal derivatives of the temperature in each phase. We establish local-in-time well-posedness and a global-in-time stability result for arbitrary sufficiently smooth domains and small initial temperatures. To this end, we develop a higher-order energy with natural weights adapted to the problem and combine it with Hopf-type inequalities. This extends the previous work by Hadzic and Shkoller [31,32] on the one-phase Stefan problem to the setting of two-phase problems, and simplifies the proof significantly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-03T20:55:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q79",
      "35B40",
      "35B65",
      "35M30"
    ],
    "keywords": [
      "two-phase stefan problem",
      "global stability",
      "local well-posedness",
      "priori unknown moving boundary",
      "global-in-time stability result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}