Curve-shortening flow of open, elastic curves in ℝ² with repelling endpoints: A minimizing movement approach

2019/02/21 by Badal, Rufat
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.08079

Abstract

We study an L²-type gradient flow of an immersed elastic curve in ℝ² 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.

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