On Asymptotic Behavior and Blow-Up of Solutions for a Nonlinear Viscoelastic Petrovsky Equation with Positive Initial Energy.

This paper deals with the initial boundary value problem for the nonlinear viscoelastic Petrovsky equation utt + Δ²u - Δt0(t - Τ)Δ²u(x,Τ)dΤ-Δut Δutt + |ut|m-1ut = |u|p-1u. Under certain conditions on g and the assumption that m < p, we establish some asymptotic behavior and blow-up results for solutions with positive initial energy. [ABSTRACT FROM AUTHOR]