{
  "id": "2008.11382",
  "version": "v1",
  "published": "2020-08-26T05:40:07.000Z",
  "updated": "2020-08-26T05:40:07.000Z",
  "title": "Boundary controllability of phase-transition region of a two-phase Stefan problem",
  "authors": [
    "Viorel Barbu"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "One proves that the moving interface of a two-phase Stefan problem on $\\ooo\\subset\\rr^d$, $d=1,2,3,$ is controllable at the end time $T$ by a Neumann boundary controller $u$. The phase-transition region is a mushy region $\\{\\sigma^u_t;\\ 0\\le t\\le T\\}$ of a modified Stefan problem and the main result amounts to saying that, for each Lebesque measurable set $\\ooo^*$ with positive measure, there is $u\\in L^2((0,T)\\times\\pp\\ooo)$ such that $\\ooo^*\\subset\\sigma^u_T.$ To this aim, one uses an optimal control approach combined with Carleman's inequality and the Kakutani fixed point theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-26T05:40:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "80A22",
      "94B05",
      "93C10"
    ],
    "keywords": [
      "two-phase stefan problem",
      "phase-transition region",
      "boundary controllability",
      "kakutani fixed point theorem",
      "optimal control approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}