{
  "id": "1705.10985",
  "version": "v1",
  "published": "2017-05-31T08:41:44.000Z",
  "updated": "2017-05-31T08:41:44.000Z",
  "title": "Metastability of the Cahn-Hilliard equation in one space dimension",
  "authors": [
    "Sebastian Scholtes",
    "Maria G. Westdickenberg"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one in energy and order-one in $\\dot{H}^{-1}$ away from a point on the so-called slow manifold with $N$ well-separated layers. Specifically, we show that, for such initial data on a system of lengthscale $\\Lambda$, there are three phases of evolution: (1) the solution is drawn after a time of order $\\Lambda^2$ into an algebraically small neighborhood of the $N$-layer branch of the slow manifold, (2) the solution is drawn after a time of order $\\Lambda^3$ into an exponentially small neighborhood of the $N$-layer branch of the slow manifold, (3) the solution is trapped for an exponentially long time exponentially close to the $N$-layer branch of the slow manifold. The timescale in phase (3) is obtained with the sharp constant in the exponential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-31T08:41:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "space dimension",
      "slow manifold",
      "layer branch",
      "metastability",
      "initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}