{
  "id": "1905.10803",
  "version": "v1",
  "published": "2019-05-26T13:27:24.000Z",
  "updated": "2019-05-26T13:27:24.000Z",
  "title": "Long time behavior of solutions of degenerate parabolic equations with inhomogeneous density on manifolds",
  "authors": [
    "Daniele Andreucci",
    "Anatoli F. Tedeev"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We consider the Cauchy problem for doubly non-linear degenerate parabolic equations on Riemannian manifolds of infinite volume, or in $\\R^N$. The equation contains a weight function as a capacitary coefficient which we assume to decay at infinity. We connect the behavior of non-negative solutions to the interplay between such coefficient and the geometry of the manifold, obtaining, in a suitable subcritical range, estimates of the vanishing rate for long times and of the finite speed of propagation. In supercritical ranges we obtain universal bounds and prove blow up in a finite time of the (initially bounded) support of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-26T13:27:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K65",
      "35B40"
    ],
    "keywords": [
      "long time behavior",
      "inhomogeneous density",
      "doubly non-linear degenerate parabolic equations",
      "finite time",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}