Special Session 150: Water Waves and Beyond

A differential inequality, an invariant set and the blow-up of high-energy solutions of a quasilinear riser equation
Jorge A Esquivel - Avila
Universidad Autonoma Metropolitana
Mexico
Co-Author(s):    
Abstract:
We consider a damped quasilinear equation of fourth order that models the mechanical vibrations of a marine riser. We study the nonexistence of global solutions, for any real value of the initial energy. For this purpose we analyze a new differential inequality and construct a new invariant set, improving the results known in the literature. We analyze the influence of the damping term on the blow-up of the solution and find a finite critical damping coefficient for which the blow-up time becomes infinite. Finally, we propose a conjecture for the existence of global solutions for any real value of the initial energy.