On the curve straightening flow of inextensible, open, planar curves

Oelz, D. (2011) On the curve straightening flow of inextensible, open, planar curves. SeMA Journal, 54 1: 5-24. doi:10.1007/BF03322585


Author Oelz, D.
Title On the curve straightening flow of inextensible, open, planar curves
Journal name SeMA Journal   Check publisher's open access policy
ISSN 2254-3902
2281-7875
Publication date 2011-01-01
Sub-type Article (original research)
DOI 10.1007/BF03322585
Open Access Status Not yet assessed
Volume 54
Issue 1
Start page 5
End page 24
Total pages 20
Publisher Springer
Language eng
Abstract We consider the curve straightening flow of inextensible, open, planar curves generated by the Kirchhoff bending energy. It can be considered as a model for the motion of elastic, inextensible rods in a high friction regime. We derive governing equations, namely a semilinear fourth order parabolic equation for the indicatrix and a second order elliptic equation for the Lagrange multiplier. We prove existence and regularity of solutions, compute the energy dissipation, prove its coercivity and conclude convergence to equilibrium, namely to a straight curve, at an exponential rate.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Sat, 14 Jan 2017, 02:23:05 EST by Kay Mackie on behalf of School of Mathematics & Physics