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-Δpu=uq,(x,t)ɛΩ×(0,T),u(x,t)=0,(x,t)ɛδΩ×(0,T),u(x,0)=u0(x),u0(x)≥0,u0(x)≡/0the 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),0ɛΩ,Δpu=div(|∇u|p-2∇u),0≤s≤2,p≥2,p-1<q<Np-N+pN-p.