Geodesic
Curve-shortening of open elastic curves with repelling endpoints: A minimizing movements approach
Rufat Badal1
1Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Interfaces and free boundaries, Tome 24 (2022) no. 3, pp. 389-430

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DOI

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.
DOI : 10.4171/ifb/475
Classification : 35-XX, 49-XX, 53-XX
Mots-clés : Geometric evolution equations, Willmore flow, minimizing movements, curve shortening flow with interacting endpoints

Rufat Badal  1

1 Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany 
Rufat Badal. Curve-shortening of open elastic curves with repelling endpoints: A minimizing movements approach. Interfaces and free boundaries, Tome 24 (2022) no. 3, pp. 389-430. doi: 10.4171/ifb/475
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     title = {Curve-shortening of open elastic curves with repelling endpoints: {A} minimizing movements approach},
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     pages = {389--430},
     year = {2022},
     volume = {24},
     number = {3},
     doi = {10.4171/ifb/475},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/475/}
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