Long-time behavior for fourth-order wave equations with strain term and nonlinear weak damping term

Abstract

<p style='text-indent:20px;'>We mainly focus on the asymptotic behavior analysis for certain fourth-order nonlinear wave equations with strain term, nonlinear weak damping term and source term. We establish two theorems on the asymptotic behavior of the solution depending on some conditions related to the relationship among the forced strain term, the nonlinear weak damping term and source terms.</p>

Improved blowup time estimates for fourth-order damped wave equations with strain term and arbitrary positive initial energy

“…Han et al [3] showed the finite time blowup of solutions for arbitrarily positive initial energy E(0) > 0. Relevant problems with damping and source terms were considered in [2,6,9,15]. Some representative works [8,12,13] studied the control mechanism of the initial data on the dynamic behavior of solutions by the potential well method.…”