Nonexistence of type II blowup solution for a semilinear heat equation

A solution u of a Cauchy problem for a semilinear heat equation{ut=Δu+|u|p−1uin RN×(0,T),u(x,0)=u0(x)in RN is said to undergo type II blowup at t=T<∞t=T<∞ iflim supt→T(T−t)1/(p−1)|u(t)|∞=∞. Let pSpS and pJLpJL be the exponents of Sobolev and of Joseph and Lundgren, respectively. We prove that when pS