{
  "id": "1608.00854",
  "version": "v1",
  "published": "2016-08-02T14:58:06.000Z",
  "updated": "2016-08-02T14:58:06.000Z",
  "title": "Global existence for a nonstandard viscous Cahn-Hilliard system with dynamic boundary condition",
  "authors": [
    "Pierluigi Colli",
    "Gianni Gilardi",
    "Jürgen Sprekels"
  ],
  "comment": "Key words: viscous Cahn-Hilliard system, phase field model, dynamic boundary conditions, well-posedness of solutions",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study a model for phase segregation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are diffcult to handle analytically. In contrast to the existing literature about this PDE system, we consider here a dynamic boundary condition involving the Laplace-Beltrami operator for the order parameter. This boundary condition models an additional nonconserving phase transition occurring on the surface of the domain. Different well-posedness results are shown, depending on the smoothness properties of the involved bulk and surface free energies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-02T14:58:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K61",
      "35A05",
      "35B40",
      "74A15"
    ],
    "keywords": [
      "nonstandard viscous cahn-hilliard system",
      "dynamic boundary condition",
      "global existence",
      "nonconserving phase transition occurring",
      "nonlinear parabolic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}