Dynamics of Elastic Wires: Preserving Area without Nonlocality

Published 7 Aug 2024 in math.AP | (2408.03823v2)

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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Authors (1)

Leonie Langer

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