{
  "id": "1302.1222",
  "version": "v1",
  "published": "2013-02-05T22:18:31.000Z",
  "updated": "2013-02-05T22:18:31.000Z",
  "title": "On solutions of the reduced model for the dynamical evolution of contact lines",
  "authors": [
    "Dmitry Pelinovsky"
  ],
  "comment": "17 pages",
  "categories": [
    "physics.flu-dyn",
    "math.AP"
  ],
  "abstract": "We solve the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180 contact angle. We use Laplace transform in spatial coordinate and Green's function for the fourth-order diffusion equation to show local existence of solutions of the initial-value problem associated with the set of over-determining boundary conditions. We also analyze the explicit solution in the case of a constant speed (dropping the additional boundary condition).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-05T22:18:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "contact line",
      "reduced model",
      "dynamical evolution",
      "linear advection-diffusion equation",
      "additional boundary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1222P"
    }
  }
}