Multiple blowup of solutions for a semilinear heat equation

The present paper is concerned with a Cauchy problem for a semilinear heat equation [inline-graphic not available: see fulltext] with u0 ∈ L∞(RN). A solution u of (P) is said to blow up at t=T<+∞ if  lim supt↗T|u(t)|∞=+∞ with the supremum norm |·|∞ in RN. We show that if [inline-graphic not available: see fulltext] and N≥11, then there exists a proper solution u of (P) which blows up at t=T1, becomes a regular solution for t ∈ (T1,T2) and blows up again at t=T2 for some T1,T2 with 0<T1<T2<+∞.