Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data

Abstract

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 -up, p > 1 and set in ℝN. We consider a bounded, nonnegative initial datum u0 that behaves like a negative power at infinity. That is, |x|αu0(x) → A > 0 as |x| → ∞ with 0 < α ≤ N. We prove that, in the supercritical case p > 1+2/α, the solution behaves asymptotically as that of the heat equation (with diffusivity a related to the nonlocal operator) with the same initial datum.