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: $$ u_{tt}+\Delta ^{2} u- \int _{0}^{t} g(t-\tau )\Delta ^{2} u(\tau )\,\mathrm{d} \tau + \vert u_{t} \vert ^{m-2}u_{t}= \vert u \vert ^{p-2}u,\quad \text{in }\varOmega \times (0,T). $$ 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 \(R\geq 0\).