Various behaviors of solutions for a semilinear heat equation after blowup

The present paper is concerned with a Cauchy problem for a semilinear heat equation u(1)=Deltau+u(p) in R-N x (0,infinity), { (P) u(x,O)=u0(x)greater than or equal to0 in R-N. We show that p > (N-2rootN-1)/(N-4-2rootN-1) and N greater than or equal to 11, then there exists a solution u(i) (i = 1, 2, 3) of (P)which blows up at t = T-i < + infinity, becomes a regular solution for all t > T-i and behaves as follows: (i) lim (t-->infinity) \u(1)(t)\infinity=0, (ii) 0 < lim inf(t-->infinity) \u2(t)\(infinity) less than or equal to lim sup(t-->infinity) \u(2)(t)\(infinity) < + infinity, (iii) lim(t-->infinity) inf(t-->infinity) \u(2)(t)\(infinity)less than or equal to lim sup(t-->infinity)\u(2)(t)\(infinity)<+infinity, where \ (.) \(infinity) denotes the supremum norm in R-N. (C) 2004 Elsevier Inc. All rights reserved.