The motion of elastic planar closed curves under the area-preserving condition
Shinya Okabe · Indiana University Mathematics Journal · 2007
Abstract. We consider the motion of an elastic closed curve with constant enclosed area. This motion is governed by a system involving fourth order parabolic equations. We shall prove that this system has a unique classical solution for all time and the solution converges uniformly to a stationary solution together with its derivatives of any order. 1.