{
  "id": "1210.5062",
  "version": "v1",
  "published": "2012-10-18T09:27:11.000Z",
  "updated": "2012-10-18T09:27:11.000Z",
  "title": "Some existence and regularity results for porous media and fast diffusion equations with a gradient term",
  "authors": [
    "Boumediene Abdellaoui",
    "Ireneo Peral",
    "Magdalena Walias"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we consider the problem $$(P)\\qquad \\{{array}{rclll} u_t-\\D u^m&=&|\\n u|^q +\\,f(x,t),&\\quad u\\ge 0 \\hbox{in} \\Omega_T\\equiv \\Omega\\times (0,T), u(x,t)&=&0 &\\quad \\hbox{on} \\partial\\Omega\\times (0,T) u(x,0)&=&u_0(x),&\\quad x\\in \\Omega {array}. $$ where $\\O\\subset \\ren$, $N\\ge 2$, is a bounded regular domain, $1<q\\le 2$, and $f\\ge 0$, $u_0\\ge 0$ are in a suitable class of functions. We obtain some results for elliptic-parabolic problems with measure data related to problem $(P)$ that we use to study the existence of solutions to problem $(P)$ according with the values of the parameters $q$ and $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-18T09:27:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fast diffusion equations",
      "gradient term",
      "regularity results",
      "porous media",
      "bounded regular domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.5062A"
    }
  }
}