Inserted: 25 oct 2012
Last Updated: 14 jan 2016
Journal: J. Differential Eqs.
We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We call the flow shortening-straightening flow.
We first prove long time existence of this flow for non-closed planar curves with infinite length. Second we show that the solution converges to a stationary solution as time goes to infinity. Moreover we give a classification of the stationary solution.