Decay and nonexistence of global solutions of a quasilinear riser equation

We study qualitative properties of a quasilinear wave equation of fourth order that models the mechanical vibrations of a marine riser. Our analysis characterizes global and nonglobal solutions with respect to the norm of some Hilbert space, if energy is strictly less than the potential well depth. We employ invariant sets to show our results. In particular, we show that globality implies exponential decay to zero, and nonglobality is due to blow up. Both results are shown with respect to the norm of the solution in the Hilbert space. Copyright © 2009 John Wiley & Sons, Ltd.