On the geometric flows of Kirchhoff elastic rods

Chun-Chi Lin and Hartmut Schwetlick

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Submission date: 29. Jun. 2003 (revised version: September 2004)
Pages: 19
published in: SIAM journal on applied mathematics, 65 (2005) 2, p. 720-736 
DOI number (of the published article): 10.1137/S0036139903431713
Bibtex
MSC-Numbers: 35K55, 53C44, 74B20, 74L15
Keywords and phrases: geometric flows, fourth order, kirchhoff elastic rods
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Abstract:
Rod theory has been applied to the modelling of DNA and bacterial fibers in their mechanics aspects. In this paper, we relate a geometric functional of curves to the simplest Kirchhoff elastic energy of rods so that the generalized elastic curves are the centerlines of elastic rods in equilibrium. Then, under a mild assumption, we derive the long time existence of the length preserving evolution of the elastic rods.