Continuous dependence on initial data for damped fourth-order wave equation with strain term

Abstract This article investigates the fourth-order wave equation with general nonlinear strain term as well as both strong and weak damping terms. By deriving and utilizing energy decay estimate independent of the initial data in the stable manifold, we derive results regarding the continuous dependence of the global solution on initial data for the model equation with such a structure. These conclusions reflect the dissipative nature of the model.