On the behavior of blow-up solutions to a parabolic problem with critical exponent

The blow-up behavior of the solution to a semilinear equation with critical exponent {ut=Δu+|u|p−1uin Ω×(0,T),u=0on ∂Ω×(0,T),u(⋅,0)=u0on Ω is established. We obtain that if ΩΩ is star-shaped about a∈Ωa∈Ω and n⩾3,p=n+2n−2, then limt→T(T−t)βu(a+yT−t,t) exists and equals 0 or ±κ±κ in Lloc2(Rn), where β=1p−1,κ=ββ.