On the blow-up of solutions for some fourth order parabolic equations

The universal blow-up of the fourth order parabolic evolution problem {ut+Δ(Δu+|u|p−1u)=0in Ω×[0,T),u=Δu=0on ∂Ω×[0,T),u=u0in Ω×{0} is established. We prove that if the energy of the initial datum is negative, then finite time blow-up occurs. Also we get some nondegeneracy results on blow-up for this problem.