{
  "id": "2203.06003",
  "version": "v1",
  "published": "2022-03-11T15:23:27.000Z",
  "updated": "2022-03-11T15:23:27.000Z",
  "title": "A singular two-phase Stefan problem and particles interacting through their hitting times",
  "authors": [
    "Graeme Baker",
    "Mykhaylo Shkolnikov"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We consider a probabilistic formulation of a singular two-phase Stefan problem in one space dimension, which amounts to a coupled system of two McKean-Vlasov stochastic differential equations. Our main result shows the existence of a solution whose discontinuities obey the natural physicality condition for the problem at hand. Thus, this work extends the recent series of existence results for singular one-phase Stefan problems in one space dimension that can be found in [DIRT15a], [NS19a], [HLS18], [CRSF20]. As therein, our existence result is obtained via a large system limit of a finite particle system approximation in the Skorokhod M1 topology. But, unlike for the previously studied one-phase case, the free boundary herein is not monotone, so that the large system limit is obtained by a novel argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-11T15:23:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C22",
      "60H30",
      "35K10",
      "35K60"
    ],
    "keywords": [
      "singular two-phase stefan problem",
      "hitting times",
      "particles interacting",
      "large system limit",
      "existence result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}