{
  "id": "1102.0941",
  "version": "v1",
  "published": "2011-02-04T15:30:13.000Z",
  "updated": "2011-02-04T15:30:13.000Z",
  "title": "Regularity of solutions to a model for solid-solid phase transitions driven by configurational forces",
  "authors": [
    "Peicheng Zhu"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In a previous work, we prove the existence of weak solutions to an initial-boundary value problem, with $H^1(\\Omega)$ initial data, for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, degenerate parabolic equation of second order. Assuming in this article the initial data is in $H^2(\\Omega)$, we investigate the regularity of weak solutions that is difficult due to the gradient term which plays a role of a weight. The problem models the behavior in time of materials with martensitic phase transitions. This model with diffusive phase interfaces was derived from a model with sharp interfaces, whose evolution is driven by configurational forces, and can be thought to be a regularization of that model. Our proof, in which the difficulties are caused by the weight in the principle term, is only valid in one space dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-04T15:30:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "74E15"
    ],
    "keywords": [
      "solid-solid phase transitions driven",
      "configurational forces",
      "regularity",
      "initial data",
      "weak solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.0941Z"
    }
  }
}