English

Curve-shortening flow of open, elastic curves in $\mathbb{R}^2$ with repelling endpoints: A minimizing movement approach

Analysis of PDEs 2019-02-22 v1

Abstract

We study an L2L^{2}-type gradient flow of an immersed elastic curve in R2\mathbb{R}^{2} whose endpoints repel each other via a Coulomb potential. By De Giorgi's minimizing movements scheme we prove long-time existence of the flow. The work is complemented by several numerical experiments.

Keywords

Cite

@article{arxiv.1902.08079,
  title  = {Curve-shortening flow of open, elastic curves in $\mathbb{R}^2$ with repelling endpoints: A minimizing movement approach},
  author = {Rufat Badal},
  journal= {arXiv preprint arXiv:1902.08079},
  year   = {2019}
}