Optimal decay rates of a nonlinear suspension bridge with memories

Abstract

In this paper, we investigate the decay properties of suspension bridge with memories in one dimension. To prove our results, we use the energy method to build some very delicate Lyapunov functionals that give the desired results.

On the internal and boundary stabilization of a nonlinear suspension bridge system: Exponential and polynomial decay rates

“…We can cite the works of [12] for the suspension bridge models with viscoelastic or memory, [23] for Kang's contribution on the global attractor to a thermoelastic suspension bridge equation with past history, and [29] for Mukiawa's contribution on the asymptotic behavior of the solutions of the suspension bridges with viscoelastic damping. Afilal et al [4] demonstrated the uniform decay of the thermoelastic suspension bridges model, and Afilal et al [2] demonstrated the general decay for the suspension bridge model with two memories.…”