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arXiv · 2408.03823

Dynamics of Elastic Wires: Preserving Area without Nonlocality

Leonie Langer
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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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Leonie Langer. 2024-08-07. Dynamics of Elastic Wires: Preserving Area without Nonlocality. https://doi.org/10.1007/s00526-025-02948-0

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