Dynamics of Elastic Wires: Preserving Area without Nonlocality
Analysis of PDEs
2025-03-21 v2
Abstract
We derive an -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.
Keywords
Cite
@article{arxiv.2408.03823,
title = {Dynamics of Elastic Wires: Preserving Area without Nonlocality},
author = {Leonie Langer},
journal= {arXiv preprint arXiv:2408.03823},
year = {2025}
}
Comments
32 pages, 2 figures. Final version. Comments are welcome!