{
  "id": "1301.0909",
  "version": "v1",
  "published": "2013-01-05T15:16:15.000Z",
  "updated": "2013-01-05T15:16:15.000Z",
  "title": "A Hilbert expansions method for the rigorous sharp interface limit of the generalized Cahn-Hilliard Equation",
  "authors": [
    "D. C. Antonopoulou",
    "G. D. Karali",
    "E. Orlandi"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider Cahn-Hilliard equations with external forcing terms. Energy decreasing and mass conservation might not hold. We show that level surfaces of the solutions of such generalized Cahn-Hilliard equations tend to the solutions of a moving boundary problem under the assumption that classical solutions of the latter exist. Our strategy is to construct approximate solutions of the generalized Cahn-Hilliard equation by the Hilbert expansion method used in kinetic theory and proposed for the standard Cahn-Hilliard equation, by Carlen, Carvalho and Orlandi, \\cite {CCO}. The constructed approximate solutions allow to derive rigorously the sharp interface limit of the generalized Cahn-Hilliard equations. We then estimate the difference between the true solutions and the approximate solutions by spectral analysis, as in \\cite {A-B-C}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-05T15:16:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rigorous sharp interface limit",
      "hilbert expansions method",
      "generalized cahn-hilliard equations tend",
      "construct approximate solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}