Losing a graph with surface diffusion (Q5945553)

The authors investigate geometric evolution of planar curves determined by a generalized surface diffusion law: \(V= - \partial_s^2 k + f(k,\theta)\), where \(V\) denotes the outward normal velocity, \(k\) is the curvature, \(\theta\) is the tangential angle and \(s\) is the arc-length of a planar curve. The main result gives that the above evolution law, starting with initially smooth graph can lead to a non-graph situation within a finite time.