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The motion of elastic planar closed curves under the area-preserving condition. (English) Zbl 1121.74009

Summary: 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 prove that this system has a unique classical solution for all time, and that the solution converges uniformly to a stationary solution together with its derivatives of any order.

MSC:

74B99 Elastic materials
74G65 Energy minimization in equilibrium problems in solid mechanics
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