On the Extinction Profile for Solutions of u(t) = Delta u((N-2)/)((N+2))

In this paper we study the Cauchy problem u(t) = Deltau((N-2)/(N+2)) in R-N x (0, infinity), (x, 0) = u(0)(x), with N greater than or equal to 3. If u0 0 0 is continuou s, nonnegative and u0 (x) = O(\x \ (-(N+2))) as \x \ --> infinity, then the solution u vanishes identically after a (least) finite time T > 0. We prov e the asymptotic formula u(x, t) similar to (T - t)((N + 2)/4) {k(N)lambda/lambda (2) + \x - (x) ove r bar \ (2)}((N+2)/2) as t up arrow T, for certain (x) over bar is an element of R-N, lambda > 0, which depend continuously on u(0) in some appropriate topology.