{
  "id": "1704.05337",
  "version": "v1",
  "published": "2017-04-18T13:41:34.000Z",
  "updated": "2017-04-18T13:41:34.000Z",
  "title": "On a Cahn-Hilliard system with convection and dynamic boundary conditions",
  "authors": [
    "Pierluigi Colli",
    "Gianni Gilardi",
    "Jürgen Sprekels"
  ],
  "comment": "Key words: Cahn-Hilliard system, convection, dynamic boundary condition, initial-boundary value problem, well-posedness, regularity of solutions",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of Cahn-Hilliard type; an additional convective term with a forced velocity field, which could act as a control on the system, is also present in the equation. Either regular or singular potentials are admitted in the bulk and on the boundary. Both the viscous and pure Cahn-Hilliard cases are investigated, and a number of results is proven about existence of solutions, uniqueness, regularity, continuous dependence, uniform boundedness of solutions, strict separation property. A complete approximation of the problem, based on the regularization of maximal monotone graphs and the use of a Faedo-Galerkin scheme, is introduced and rigorously discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-18T13:41:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K61",
      "35K25",
      "76R05",
      "80A22"
    ],
    "keywords": [
      "dynamic boundary conditions",
      "cahn-hilliard system",
      "convection",
      "boundary value problem",
      "pure cahn-hilliard cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}