Multiple blowup of solutions for a semilinear heat equation II

[摘要] The present paper is concerned with a Cauchy problem for a semilinear heat equation u(t) = Delta u + u(p) in R-N x (0, infinity), u(x, 0) = u(0)(x) >= 0 in R-N with p > 1 and u(0) is an element of L-infinity(R-N). We show that if p > N-2 root N-1/ N-4-2 root N-1 and N >= 11 , then for each positive integer n >= 2 there exist T-i > 0, i = 1, 2..... n, with T-1 < T-2 < ... < T-n < + infinity and a global L-1-solution u of (P) such that u is a regular solution of (P) for t is an element of [0, infinity)\ {T-1, T-2,. T-n} and blows up at t = T-i for i = 1, 2,..., n. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-01

[关键词] semilinear heat equation;supercritical;incomplete blowup;multiple blowup