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Dynamics of Elastic Wires: Preserving Area without Nonlocality (2408.03823v2)
Published 7 Aug 2024 in math.AP
Abstract: We derive an $H{-1}$-gradient flow of the elastic energy which preserves the enclosed area of evolving planar curves. For this new sixth-order evolution equation, we prove a global existence result. Additionally, by penalizing the length, we show convergence to an area constrained critical point of the elastic energy.
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