{
  "id": "1102.0939",
  "version": "v1",
  "published": "2011-02-04T15:24:59.000Z",
  "updated": "2011-02-04T15:24:59.000Z",
  "title": "Spherically symmetric solutions to a model for phase transitions driven by con?figurational forces",
  "authors": [
    "Yaobin Ou",
    "Peicheng Zhu"
  ],
  "comment": "25 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, non-uniformly parabolic equation of second order. The problem models the behavior in time of materials in which martensitic phase transitions, driven by configurational forces, take place, and can be considered to be a regularization of the corresponding sharp interface model. By assuming that the solutions are spherically symmetric, we reduce the original multidimensional problem to the one in one space dimension, then prove the existence of spherically symmetric solutions. Our proof is valid due to the essential feature that the reduced problem is one space dimensional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-04T15:24:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "74E15",
      "05.70.Fh",
      "02.30.Jr",
      "02.60.Lj"
    ],
    "keywords": [
      "spherically symmetric solutions",
      "phase transitions driven",
      "figurational forces",
      "partial differential equations",
      "original multidimensional problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.3640040",
      "journal": "Journal of Mathematical Physics",
      "year": 2011,
      "month": "Sep",
      "volume": 52,
      "number": 9,
      "pages": 3708
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JMP....52i3708O"
    }
  }
}