Existence and blow up of solution for a Petrovsky equations of Hartree type

This is the authors' abstract. We don't add key points for this paper.

In this work, we establish the initial boundary value problem of a class of Petrovsky equation of Hartree-type. We prove the global existence of weak solutions by applying potential well theory. Furthermore, we investigate the blow-up phenomena of solutions under nonnegative or negative initial energy conditions.