Asymptotic behavior of global solutions of a semilinear parabolic problem

We study the asymptotic behavior of nonnegative solutions of the semilinear parabolic problem {ut=Δu+up,x∈RN,t>0u(0)=u0,x∈RN,t=0. It is known that the nonnegative solution u(t)u(t) of this problem blows up in finite time for 11+2/Np>1+2/N and the norm of u0u0 is small enough, the problem admits a global solution. In this work, we use the entropy method to obtain the decay rate of the global solution u(t)u(t).