{
  "id": "1705.07033",
  "version": "v1",
  "published": "2017-05-19T14:50:11.000Z",
  "updated": "2017-05-19T14:50:11.000Z",
  "title": "Maximal monotone operator in non-reflexive Banach space and the application to thin film equation in epitaxial growth on vicinal surface",
  "authors": [
    "Yuan Gao",
    "Jian-Guo Liu",
    "Xin Yang Lu",
    "Xiangsheng Xu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work we consider $$ w_t=[(w_{hh}+c_0)^{-3}]_{hh},\\qquad w(0)=w^0, $$ which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. The mathematical difficulty is due to the fact that $w_{hh}$ can appear as a positive Radon measure. We prove the existence of a global strong solution. In particular, the equation holds almost everywhere when $w_{hh}$ is replaced by its absolutely continuous part.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-19T14:50:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thin film equation",
      "non-reflexive banach space",
      "vicinal surface",
      "epitaxial growth",
      "maximal monotone operator theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}