English

Dynamics of Elastic Wires: Preserving Area without Nonlocality

Analysis of PDEs 2025-03-21 v2

Abstract

We derive an H1H^{-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.

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!