{
  "id": "1004.0717",
  "version": "v2",
  "published": "2010-04-05T21:03:23.000Z",
  "updated": "2010-04-12T20:31:24.000Z",
  "title": "Large Time Behavior of a Nonlocal Diffusion Equation with Absorption and Bounded Initial Data",
  "authors": [
    "Joana Terra",
    "Noemi Wolanski"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the large time behavior of nonnegative solutions of the Cauchy problem $u_t=\\int J(x-y)(u(y,t)-u(x,t))\\,dy-u^p$, $u(x,0)=u_0(x)\\in L^\\infty$, where $|x|^{\\alpha}u_0(x)\\to A>0$ as $|x|\\to\\infty$. One of our main goals is the study of the critical case $p=1+2/\\alpha$ for $0<\\alpha<N$, left open in previous articles, for which we prove that $t^{\\alpha/2}|u(x,t)-U(x,t)|\\to 0$ where $U$ is the solution of the heat equation with absorption with initial datum $U(x,0)=C_{A,N}|x|^{-\\alpha}$. Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data $u_0$ in the supercritical case and also in the critical case ($p=1+2/N$) for bounded and integrable $u_0$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-04-12T20:31:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial datum",
      "large time behavior",
      "nonlocal diffusion equation",
      "bounded initial data",
      "absorption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.0717T"
    }
  }
}