{
  "id": "1307.1410",
  "version": "v1",
  "published": "2013-07-04T17:00:07.000Z",
  "updated": "2013-07-04T17:00:07.000Z",
  "title": "A nonlocal two phase Stefan problem",
  "authors": [
    "Emmanuel Chasseigne",
    "Silvia Sastre-Gomez"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for sign-changing solutions of the equation, ut = J * v - v, v = {\\Gamma}(u), where the monotone graph is given by {\\Gamma}(s) = sign(s)(|s|-1)+ . We give general results of existence, uniqueness and comparison, in the spirit of [2]. Then we focus on the study of the asymptotic behaviour for sign-changing solutions, which present challenging difficulties due to the non-monotone evolution of each phase.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-04T17:00:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sign-changing solutions",
      "distinct heat equations",
      "phase transition problem",
      "two-phase stefan problem",
      "nonlocal version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1410C"
    }
  }
}