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Curve-shortening of open elastic curves with repelling endpoints: a minimizing movements approach. (English) Zbl 1497.35296

Summary: We study an \(L^2\)-type gradient flow of an immersed elastic curve in \(\mathbb{R}^2\) 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.

MSC:

35K30 Initial value problems for higher-order parabolic equations
35A15 Variational methods applied to PDEs
53E40 Higher-order geometric flows
49J10 Existence theories for free problems in two or more independent variables

Software:

JuMP; Julia; Ipopt
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References:

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