{
  "id": "1804.09645",
  "version": "v1",
  "published": "2018-04-25T16:01:08.000Z",
  "updated": "2018-04-25T16:01:08.000Z",
  "title": "Global existence and decay to equilibrium for some crystal surface models",
  "authors": [
    "Rafael Granero-Belinchón",
    "Martina Magliocca"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the large time behavior of the solutions to the following nonlinear fourth-order equations $$ \\partial_t u=\\Delta e^{-\\Delta u}, $$ $$ \\partial_t u=-u^2\\Delta^2(u^3). $$ These two PDE were proposed as models of the evolution of crystal surfaces by J. Krug, H.T. Dobbs, and S. Majaniemi (Z. Phys. B, 97, 281-291, 1995) and H. Al Hajj Shehadeh, R. V. Kohn, and J. Weare (Phys. D, 240, 1771-1784, 2011), respectively. In particular, we find explicitly computable conditions on the size of the initial data (measured in terms of the norm in a critical space) guaranteeing the global existence and exponential decay to equilibrium in the Wiener algebra and in Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-25T16:01:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "crystal surface models",
      "global existence",
      "equilibrium",
      "large time behavior",
      "nonlinear fourth-order equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}