{
  "id": "1310.0965",
  "version": "v1",
  "published": "2013-10-03T12:59:27.000Z",
  "updated": "2013-10-03T12:59:27.000Z",
  "title": "Non-isothermal viscous Cahn--Hilliard equation with inertial term and dynamic boundary conditions",
  "authors": [
    "Cecilia Cavaterra",
    "Maurizio Grasselli",
    "Hao Wu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a non-isothermal modified Cahn--Hilliard equation which was previously analyzed by M. Grasselli et al. Such an equation is characterized by an inertial term and a viscous term and it is coupled with a hyperbolic heat equation. The resulting system was studied in the case of no-flux boundary conditions. Here we analyze the case in which the order parameter is subject to a dynamic boundary condition. This assumption requires a more refined strategy to extend the previous results to the present case. More precisely, we first prove the well-posedness for solutions with bounded energy as well as for weak solutions. Then we establish the existence of a global attractor. Finally, we prove the convergence of any given weak solution to a single equilibrium by using a suitable Lojasiewicz--Simon inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-03T12:59:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B41",
      "37L99",
      "80A22"
    ],
    "keywords": [
      "dynamic boundary condition",
      "non-isothermal viscous cahn-hilliard equation",
      "inertial term",
      "weak solution",
      "hyperbolic heat equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.0965C"
    }
  }
}