Stabilization of solutions of marine riser equations

Abstract

We study the problem of stabilization to zero stationary state of nonlinear fourth-order wave equation with nonlinear damping term modelling dynamics of marine riser by feedback control terms that employ finitely many Fourier modes. Additionally, we demonstrate that the corresponding equation with linear damping, which represents the dynamics of pipes conveying fluids, can be exponentially stabilized by a feedback controller employing a finite number of Fourier modes.