Finite time blow-up for a class of parabolic or pseudo-parabolic equations

In this paper, we study the initial boundary value problem for a class of parabolic or pseudo-parabolic equations: ut−aΔut−Δu+bu=k(t)|u|p−2u,(x,t)∈Ω×(0,T),where a≥0, b>−ł1 with ł1 being the principal eigenvalue for −Δ on H01(Ω) and k(t)>0. By using the potential well method, Levine's concavity method and some differential inequality techniques, we obtain the finite time blow-up results provided that the initial energy satisfies three conditions: (i) J(u0;0)<0; (ii) J(u0;0)≤d(∞), where d(∞) is a nonnegative constant; (iii) 0