THE EXISTENCE OF GLOBAL SOLUTION AND THE BLOWUP PROBLEM FOR SOME p-LAPLACE HEAT EQUATIONS

This article consider, for the following heat equation {ut/|x|s-△pu=uq,(x,t) ∈ Ω×(0,T),u(x,t)=0,(x,t) ∈(δ)Ω×(0,T),u(x,0) =u0(x), u0(x)≥0,u0(x) (≠)0 the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, where Ω is a smooth bounded domain in RN(N＞p),0 ∈ Ω,△pu=div(|▽u|p-2▽u),0 ≤s≤2,p≥2,p-1＜q＜Np-Np+p/N-p.