Asymptotic Behavior for a Nonlocal Diffusion Equation with Absorption and Nonintegrable Initial Data. the Supercritical Case

In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction \(-u^p\), \(p>1\) and set in \(\R^N\). We consider a bounded, nonnegative initial datum \(u_0\) that behaves like a negative pow...

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Bibliographic Details
Published in:arXiv.org 2010-06
Main Authors: Terra, Joana, Wolanski, Noemi
Format: Article
Language:English
Subjects:
Absorption
Asymptotic properties
Datum (elevation)
Infinity
Thermodynamics
Online Access:Get full text
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Summary:In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction \(-u^p\), \(p>1\) and set in \(\R^N\). We consider a bounded, nonnegative initial datum \(u_0\) that behaves like a negative power at infinity. That is, \(|x|^\alpha u_0(x)\to A>0\) as \(|x|\to\infty\) with \(01+2/\alpha\), the solution behaves asymptotically as that of the heat equation --with diffusivity \(\a\) related to the nonlocal operator-- with the same initial datum.
ISSN:2331-8422