On the Extinction Profile for Solutions of ut= Δu(N−2)/(N+2)

In this paper we study the Cauchy problem ut = Δu(N−2)/(N+2) in ℝN × (0, ∞), u(x,0) = u0(x), with N ≥ 3. If u0 ≢ 0 is continuous, nonnegative and u0(x) = O(|x|−(N+2)) as |x| → ∞, then the solution u vanishes identically after a (least) finite time T > 0. We prove the asymptotic formula $u(x,t)\sim (T-t)^{(N+2)/4}\left \{ \right.\frac{k_N\lambda }{\lambda ^2+|x-\bar{x}|^2}\left. \right \}^{(N+2)/2}$ as t ↑ T, for certain x̄ ∈ ℝN, λ > 0, which depend continuously on u0 in some appropriate topology.