{
  "id": "1609.05853",
  "version": "v1",
  "published": "2016-09-19T18:39:13.000Z",
  "updated": "2016-09-19T18:39:13.000Z",
  "title": "Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime",
  "authors": [
    "Yuan Gao",
    "Jian-Guo Liu",
    "Jianfeng Lu"
  ],
  "comment": "Epitaxial growth, thin film, global existence, long-time behavior, fourth-order degenerate parabolic equation, BCF step dynamics",
  "categories": [
    "math.AP",
    "nlin.AO"
  ],
  "abstract": "We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, $ u_t=-u^2(u^3)_{hhhh}$, where $u$, considered as a function of step height $h$, is the step slope of the surface. We formulate a notion of weak solution to this continuum model and prove the existence of a global weak solution, which is positive almost everywhere. We also study the long time behavior of weak solution and prove it converges to a constant solution as time goes to infinity. The space-time H\\\"older continuity of the weak solution is also discussed as a byproduct.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-19T18:39:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuum model",
      "vicinal surface",
      "attachment-detachment-limited regime",
      "long time behavior",
      "type step flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}