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

TL;DR

This paper studies the stability and decay behavior of the nonlinear marine riser equation with time-dependent boundary conditions and coefficients, establishing conditions for global asymptotic stability of the zero solution.

Contribution

It introduces conditions on time-dependent data that ensure the system's structural stability and decay, extending understanding of marine riser dynamics with variable parameters.

Findings

Conditions for stability depend on growth rates of boundary data

Maximum growth rates for stability are derived

Zero solution is shown to be globally asymptotically stable under these conditions

Abstract

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.