{
  "id": "1102.5691",
  "version": "v1",
  "published": "2011-02-28T15:41:48.000Z",
  "updated": "2011-02-28T15:41:48.000Z",
  "title": "Positive speed of propagation in a semilinear parabolic interface model with unbounded random coefficients",
  "authors": [
    "Patrick W Dondl",
    "Michael Scheutzow"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We consider a model for the propagation of a driven interface through a random field of obstacles. The evolution equation, commonly referred to as the Quenched Edwards-Wilkinson model, is a semilinear parabolic equation with a constant driving term and random nonlinearity to model the influence of the obstacle field. For the case of isolated obstacles centered on lattice points and admitting a random strength with exponential tails, we show that the interface propagates with a finite velocity for sufficiently large driving force. The proof consists of a discretization of the evolution equation and a supermartingale estimate akin to the study of branching random walks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-28T15:41:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K58",
      "35R60"
    ],
    "keywords": [
      "semilinear parabolic interface model",
      "unbounded random coefficients",
      "propagation",
      "evolution equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5691D"
    }
  }
}