Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level

In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, nonlinear weak damping, and a superlinear source: u t t + Δ 2 u − ∫ 0 t g ( t − τ ) Δ 2 u ( τ ) d τ + | u t | m − 2 u t = | u | p − 2 u , in Ω × ( 0 , T ) . When the source is stronger than dissipations, we obtain the existence of certain weak solutions which blow up in finite time with initial energy E ( 0 ) = R for any given R ≥ 0 .