{
  "id": "1007.2915",
  "version": "v2",
  "published": "2010-07-17T10:05:22.000Z",
  "updated": "2012-07-18T16:44:41.000Z",
  "title": "Homogenization of the Peierls-Nabarro model for dislocation dynamics",
  "authors": [
    "Régis Monneau",
    "Stefania Patrizi"
  ],
  "comment": "39 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with a result of homogenization of an integro-differential equation describing dislocation dynamics. Our model involves both an anisotropic L\\'{e}vy operator of order 1 and a potential depending periodically on $u/\\ep$. The limit equation is a non-local Hamilton-Jacobi equation, which is an effective plastic law for densities of dislocations moving in a single slip plane.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-18T16:44:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "peierls-nabarro model",
      "homogenization",
      "integro-differential equation describing dislocation dynamics",
      "non-local hamilton-jacobi equation",
      "single slip plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2915M"
    }
  }
}