The Ill-Posed Problem Of A Cable In Compression

The linear and nonlinear dynamics of perfectly flexible cables under compression constitute an ill-posed problem. The linear problem is subject to an explosive instability, which renders any numerically obtained solution meaningless. The nonlinear problem is subject to a similar explosive instability characterized by short travelling waves of unbounded growth. The introduction of additional terms, which must include higher spatial derivatives, is essential to ensure a well-posed problem.