A priori estimates for global solutions of semilinear heat equations in RnRn

We give the a priori estimate for the global solution of the Cauchy problem ut−Δu+u=|u|p−1uut−Δu+u=|u|p−1u in Rn×(0,+∞)Rn×(0,+∞) with superlinear and subcritical growth.