{
  "id": "math/0611134",
  "version": "v1",
  "published": "2006-11-06T09:55:03.000Z",
  "updated": "2006-11-06T09:55:03.000Z",
  "title": "Asymptotic behavior of a nonisothermal viscous Cahn-Hilliard equation with inertial term",
  "authors": [
    "Maurizio Grasselli",
    "Hana Petzeltova",
    "Giulio Schimperna"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "We consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an inertial term $\\chi_{tt}$, $\\chi$ being the order parameter, which is linearly coupled with an evolution equation for the (relative) temperature $\\teta$. The latter can be of hyperbolic type if the Cattaneo-Maxwell heat conduction law is assumed. The state variables and the chemical potential are subject to the homogeneous Neumann boundary conditions. We first provide conditions which ensure the well-posedness of the initial and boundary value problem. Then, we prove that the corresponding dynamical system is dissipative and possesses a global attractor. Moreover, assuming that the nonlinear potential is real analytic, we establish that each trajectory converges to a single steady state by using a suitable version of the Lojasiewicz-Simon inequality. We also obtain an estimate of the decay rate to equilibrium.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-06T09:55:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B41",
      "35R35",
      "80A22"
    ],
    "keywords": [
      "nonisothermal viscous cahn-hilliard equation",
      "inertial term",
      "asymptotic behavior",
      "nonisothermal fast phase separation",
      "fast phase separation processes"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2007.05.003",
      "journal": "Journal of Differential Equations",
      "year": 2007,
      "volume": 239,
      "number": 1,
      "pages": 38
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007JDE...239...38G"
    }
  }
}