{
  "id": "1801.01784",
  "version": "v1",
  "published": "2018-01-05T15:15:48.000Z",
  "updated": "2018-01-05T15:15:48.000Z",
  "title": "Vanishing Viscosity Limits of Scalar Equations with Degenerate Diffusivity",
  "authors": [
    "Giuseppe Coclite",
    "Andrea Corli",
    "Lorenzo di Ruvo"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a scalar, possibly degenerate parabolic equation with a source term, in several space dimensions. For initial data with bounded variation we prove the existence of solutions to the initial-value problem. Then we show that these solutions converge, in the vanishing-viscosity limit, to the Kruzhkov entropy solution of the corresponding hyperbolic equation. The proof exploits the H-measure compactness in several space dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-05T15:15:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K65",
      "35L65",
      "35B25"
    ],
    "keywords": [
      "vanishing viscosity limits",
      "scalar equations",
      "degenerate diffusivity",
      "space dimensions",
      "possibly degenerate parabolic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}