  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. In this paper, first
we prove a long time existence result for the shortening-straightening flow for
non-closed planar curves with infinite length. Then we show that the solution
converges to a stationary solution as time goes to infinity. Moreover we give a
classification of the stationary solution.
