{
  "id": "0902.1816",
  "version": "v1",
  "published": "2009-02-11T07:47:42.000Z",
  "updated": "2009-02-11T07:47:42.000Z",
  "title": "Convergence of perturbed Allen-Cahn equations to forced mean curvature flow",
  "authors": [
    "Luca Mugnai",
    "Matthias Röger"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We study perturbations of the Allen-Cahn equation and prove the convergence to forced mean curvature flow in the sharp interface limit. We allow for perturbations that are square-integrable with respect to the diffuse surface area measure. We give a suitable generalized formulation for forced mean curvature flow and apply previous results for the Allen-Cahn action functional. Finally we discuss some applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-11T07:47:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "35K55",
      "49Q15"
    ],
    "keywords": [
      "forced mean curvature flow",
      "perturbed allen-cahn equations",
      "convergence",
      "diffuse surface area measure",
      "sharp interface limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.1816M"
    }
  }
}