{
  "id": "1107.0896",
  "version": "v1",
  "published": "2011-07-05T15:10:20.000Z",
  "updated": "2011-07-05T15:10:20.000Z",
  "title": "Travelling graphs for the forced mean curvature motion in an arbitrary space dimension",
  "authors": [
    "Régis Monneau",
    "Jean-Michel Roquejoffre",
    "Violaine Roussier-Michon"
  ],
  "comment": "36 pages, 6 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct travelling wave graphs of the form $z=-ct+\\phi(x)$, $\\phi: x \\in \\mathbb{R}^{N-1} \\mapsto \\phi(x)\\in \\mathbb{R}$, $N \\geq 2$, solutions to the $N$-dimensional forced mean curvature motion $V_n=-c_0+\\kappa$ ($c\\geq c_0$) with prescribed asymptotics. For any 1-homogeneous function $\\phi_{\\infty}$, viscosity solution to the eikonal equation $|D\\phi_{\\infty}|=\\sqrt{(c/c_0)^2-1}$, we exhibit a smooth concave solution to the forced mean curvature motion whose asymptotics is driven by $\\phi_{\\infty}$. We also describe $\\phi_{\\infty}$ in terms of a probability measure on $\\mathbb{S}^{N-2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-05T15:10:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary space dimension",
      "travelling graphs",
      "dimensional forced mean curvature motion",
      "smooth concave solution",
      "construct travelling wave graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.0896M"
    }
  }
}