Abstract

In this paper we study the Cauchy problem ut = ?u(N-2)/(N+2) in ?N × (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) ? (T - t)(N+2)/4{kN?/?2 + |x - x?|2}(N+2)/2 as t ? T, for certain x? ? ?N, ? > 0, which depend continuously on u0 in some appropriate topology.