锥退化半线性抛物方程的整体存在性与非存在性

his article considered the initial boundary value problem ofsemilinear parabolic equations ut-ΔBu=|u|p-1 u onmanifold with conical singularity, where ΔB is Fuchstype operator with totally characteristic degeneracy on the boundary x1=0. By using a family ofpotential wells, existence theorem of global solutions and the blow-up in finite time ofsolutions have been proved. Especially the relation between the above two phenomenais derived as a sharp condition.