The shrinking figure eight and other solitons for the curve diffusion flow

Authors

Maureen Edwards, University of WollongongFollow
Alexander Gerhardt-Bourke, University Of WollongongFollow
James A. McCoy, University of WollongongFollow
Glen Wheeler, University of WollongongFollow
V. -M Wheeler, University of WollongongFollow

RIS ID

94614

Publication Details

Edwards, M., Gerhardt-Bourke, A., McCoy, J., Wheeler, G. & Wheeler, V. (2015). The shrinking figure eight and other solitons for the curve diffusion flow. Journal of Elasticity, 119 (1-2), 191-211.

Abstract

In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This reduces to studying the curve diffusion flow for the profile curve of the ribbon. We provide: (1) a complete classification of stationary solutions; (2) qualitative results on shrinkers, translators, and rotators; and (3) an explicit parametrisation of a shrinking figure eight curve.

Grant Number

ARC/DP120100097

Additional Grant Number

http://purl.org/au-research/grants/arc/DP120100097