Structural stability and decay estimate for marine riser equations

Structural stability analysis of solutions to the initial boundary value problem for a nonlinear strongly damped wave equation

“…Different conclusions were obtained in many other articles [2,7,10,13,15,16]. References [1,[3][4][5]12] can be given for more information on the structural stability result for interested readers.…”

“…In [3], the authors considered the long-time behavior of a strongly damped nonlinear wave equation and showed that the initial boundary value problem has a global solution and that there exists a compact global attractor with finite dimension.…”

A further study on the coupled Allen–Cahn/Cahn–Hilliard equations

“…The large time behavior and the structural stability of solutions are important for the study of a higher-order parabolic system. Many papers have already been published to study the decay and the structural stability of solutions [7][8][9]. In this paper, we consider the asymptotic behavior of solutions and the continuous dependence of solutions for system (1.1)-(1.4).…”

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.…”

“…In [1], the globally asymptotically stability of the zero solution to the problem for multidimensional marine riser equation:…”