{
  "id": "2502.05545",
  "version": "v1",
  "published": "2025-02-08T12:18:07.000Z",
  "updated": "2025-02-08T12:18:07.000Z",
  "title": "Relationship among solutions for three-phase change problems with Robin, Dirichlet, and Neumann boundary conditions",
  "authors": [
    "Julieta Bollati",
    "María Fernanda Natale",
    "José Abel Semitiel",
    "Domingo Alberto Tarzia"
  ],
  "comment": "21 pages, 5 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "This study investigates the melting process of a three-phase Stefan problem in a semi-infinite material, imposing a convective boundary condition at the fixed face. By employing a similarity-type transformation, the problem is reduced to a solvable form, yielding a unique explicit solution. The analysis uncovers significant equivalences among the solutions of three different three-phase Stefan problems: one with a Robin boundary condition, another with a Dirichlet boundary condition, and a third one with a Neumann boundary condition at the fixed face. These equivalences are established under the condition that the problem data satisfy a specific relationship, providing new insights into the behaviour of phase change problems under varying boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-08T12:18:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neumann boundary condition",
      "three-phase change problems",
      "three-phase stefan problem",
      "relationship",
      "analysis uncovers significant equivalences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}