{
  "id": "1206.1583",
  "version": "v1",
  "published": "2012-06-07T19:13:27.000Z",
  "updated": "2012-06-07T19:13:27.000Z",
  "title": "Asymptotic behaviour of the doubly nonlinear equation $u_t=Δ_p u^m$ on bounded domains",
  "authors": [
    "Diana Stan",
    "Juan Luis Vazquez"
  ],
  "comment": "47 pages, 4 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the homogeneous Dirichlet problem for the doubly nonlinear equation $u_t = \\Delta_p u^m$, where $p>1,\\ m>0$ posed in a bounded domain in $\\mathbb{R}^N$ with homogeneous boundary conditions and with non-negative and integrable data. In this paper we consider the degenerate case $m(p-1)>1$ and the quasilinear case $m(p-1)=1$. We establish the large-time behaviour by proving the uniform convergence to a unique asymptotic profile and we also give rates for this convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-07T19:13:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35K55"
    ],
    "keywords": [
      "doubly nonlinear equation",
      "bounded domain",
      "asymptotic behaviour",
      "degenerate case",
      "homogeneous boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.1583S"
    }
  }
}