Higher order equations related to thin films: Blow-up and global existence, the influence of the initial data

If h0⩾0 blow-up should occur in this case. We show this fact under the Dirichlet boundary conditions for the weak solution of (KSDV)00β. The blow up time Tmax⩽−1λ13βln(1−λ1βh0φ1¯)=t∗, assuming h0φ1¯>λ1β, limt→Tmax∫0t|h(σ)|L1(]−1,+1[)6dσ=+∞.