Blowup rate of solutions for a semilinear heat equation with the Neumann boundary condition

Let p>1 and Ω be a smoothly bounded domain in RN. This paper is concerned with a Cauchy–Neumann problem We show that if u blows up at t=T, then (*) u(t)∞ C(T−t)−1/(p−1) in (0,T)with some C>0 under some condition on the Cauchy problem for the equation in (P). In particular, (*) holds if (N−1)2p