{
  "id": "1201.4920",
  "version": "v1",
  "published": "2012-01-24T07:55:11.000Z",
  "updated": "2012-01-24T07:55:11.000Z",
  "title": "Traveling Wave Solutions of Advection-Diffusion Equations with Nonlinear Diffusion",
  "authors": [
    "Léonard Monsaingeon",
    "Alexeï Novikov",
    "Jean-Michel Roquejoffre"
  ],
  "comment": "40 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds c {\\in}]c*, +{\\infty}, where c* > 0 is explicitly computed but may not be optimal. We also prove that a free boundary hy- persurface separates a region where u = 0 and a region where u > 0, and that this free boundary can be globally parametrized as a Lipschitz continuous graph under some additional non-degeneracy hypothesis; we investigate solutions which are, in the region u > 0, planar and linear at infinity in the propagation direction, with slope equal to the propagation speed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-24T07:55:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "traveling wave solutions",
      "advection-diffusion equations",
      "nonlinear diffusion",
      "nonlinear parabolic degenerate diffusion equation",
      "free boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013AnIHP..30..705M"
    }
  }
}