{
  "id": "1509.03130",
  "version": "v1",
  "published": "2015-09-10T12:50:11.000Z",
  "updated": "2015-09-10T12:50:11.000Z",
  "title": "On some degenerate non-local parabolic equation associated with the fractional $p$-Laplacian",
  "authors": [
    "Ciprian G. Gal",
    "Mahamadi Warma"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a degenerate parabolic equation associated with the fractional $% p $-Laplace operator $\\left( -\\Delta \\right) _{p}^{s}$\\ ($p\\geq 2$, $s\\in \\left( 0,1\\right) $) and a monotone perturbation growing like $\\left\\vert s\\right\\vert ^{q-2}s,$ $q>p$ and with bad sign at infinity as $\\left\\vert s\\right\\vert \\rightarrow \\infty $. We show the existence of locally-defined strong solutions to the problem with any initial condition $u_{0}\\in L^{r}(\\Omega )$ where $r\\geq 2$ satisfies $r>N(q-p)/sp$. Then, we prove that finite time blow-up is possible for these problems in the range of parameters provided for $r,p,q$ and the initial datum $u_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-10T12:50:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35K55",
      "35K65"
    ],
    "keywords": [
      "degenerate non-local parabolic equation",
      "fractional",
      "degenerate parabolic equation",
      "finite time blow-up",
      "monotone perturbation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150903130G"
    }
  }
}