On the geometric flows of Kirchhoff elastic rods
Chun-Chi Lin and Hartmut Schwetlick
Contact the author: Please use for correspondence this email.
Submission date: 29. Jun. 2003 (revised version: September 2004)
published in: SIAM journal on applied mathematics, 65 (2005) 2, p. 720-736
DOI number (of the published article): 10.1137/S0036139903431713
MSC-Numbers: 35K55, 53C44, 74B20, 74L15
Keywords and phrases: geometric flows, fourth order, kirchhoff elastic rods
Download full preprint: PDF (279 kB), PS ziped (264 kB)
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.