Stability and decay estimates for the marine riser equation in the presence of time dependent data

In this article we investigate the dynamics of the initial-boundary value problem for the nonlinear marine riser equation in the presence of time dependent boundary conditions at the top end and a time dependent coefficient of the nonlinear drag force. We introduce sufficient conditions on these functions to maintain the structural stability of the system. We deduce their maximum rates of growth to guarantee that the zero solution is globally asymptotically stable.