Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case

TERRA, JOANA; WOLANSKI, NOEMI

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Año: 2011 vol. 139 p. 1421 - 1432

0002-9939

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, $|x|^alpha u_0(x) o A>0$ as $|x| oinfty$ 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.