{
  "id": "2207.08907",
  "version": "v1",
  "published": "2022-07-18T19:54:36.000Z",
  "updated": "2022-07-18T19:54:36.000Z",
  "title": "A Class of Moving Boundary Problems with a Source Term. Application of a Reciprocal Transformation",
  "authors": [
    "Adriana C. Briozzo",
    "Colin Rogers",
    "Domingo A. Tarzia"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems for the nonlinear canonical evolution equation involving a source term with two free boundaries. This equivalence is obtained by applying a reduction to a Burgers equation and a reciprocal-type transformations. Moreover, for a particular case, we obtain a unique explicit solution for the two different problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-18T19:54:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moving boundary problems",
      "source term",
      "reciprocal transformation",
      "application",
      "unique explicit solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}