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

Abstract

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: utt+Δ2u−∫0tg(t−τ)Δ2u(τ)dτ+|ut|m−2ut=|u|p−2u,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.