Global Asymptotic Stability of Solutions to Nonlinear Marine Riser Equation

Abstract

This paper studies initial boundary value problem of fourth-order nonlinear marine riser equation. By using multiplier method, it is proven that the zero solution of the problem is globally asymptotically stable.

Energy decay rate of the solutions of a marine riser equation with a variable coefficient

“…This equation without the variable damping coe¢ cient is studied in [1] and [2]. This problem about the o¤shore drilling operations which done by a long slender vertical pipe that is including a drilling string and drilling mud, which is so called Marine riser.…”

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

“…A more general model with higher order of nonlinearity and spatial dependent coefficient of effective tension was considered in [7], where the authors managed to prove that the zero solution is globally asymptotic stable and they deduced the rate of decay of the solution when t → ∞. Extension of these results to the multidimensional case was established in [5]. Continuous dependence of the solution on the parameters of the problem was shown in [4].…”