{
  "id": "0801.4798",
  "version": "v1",
  "published": "2008-01-30T23:31:11.000Z",
  "updated": "2008-01-30T23:31:11.000Z",
  "title": "Asymptotic behavior of global solutions of the $u_t=Δu + u^{p}$",
  "authors": [
    "Oscar A. Barraza",
    "Laura B. Langoni"
  ],
  "comment": "15",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the asymptotic behavior of nonnegative solutions of the semilinear parabolic problem {u_t=\\Delta u + u^{p}, x\\in\\mathbb{R}^{N}, t>0 u(0)=u_{0}, x\\in\\mathbb{R}^{N}, t=0. It is known that the nonnegative solution $u(t)$ of this problem blows up in finite time for $1<p\\leq 1+ 2/N$. Moreover, if $p> 1+ 2/N$ and the norm of $u_{0}$ is small enough, the problem admits global solution. In this work, we use the entropy method to obtain the decay rate of the global solution $u(t)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-30T23:31:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B35",
      "35K65",
      "35K55"
    ],
    "keywords": [
      "asymptotic behavior",
      "problem admits global solution",
      "nonnegative solution",
      "semilinear parabolic problem",
      "problem blows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}