Formation of singularities in the motion of plane curves under hyperbolic mean curvature flow (Q842890)

The paper is dealing with a class of hyperbolic mean-curvature flows for plane curves. The flow depends on the temporal variable and one coordinate. An effective quasi-linear equation is derived for the description of the motion of plane curves. Using the quasi-linear equation, the formation of singularities (blowup) in the evolution of the plane waves is studied. It is proven that the formation of the singularities in a finite evolution time is a generic outcome of the evolution of periodic curves with small initial variations per period and small initial velocities. Estimates for the life-span of the general solutions are derived.