Otto-von-Guericke-Universität Magdeburg

 
 
 
 
 
 
 
 

11-19

by Wheeler, Glen

 

Preprint series: 11-19, Preprints

MSC:
35G25 Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations

 

Abstract: In this paper we consider the steepest descent H-1 gradient flow of the length functional for immersed plane curves, known as the curve diffusion flow. We prove that under the flow closed or complete periodic curves with initial data close to a multiply-covered circle or straight line respectively. In the first case we also provide an estimate for the time during which the curvature is not strictly positive. As an application of these results we obtain a rigidity statement for immersed planar curves.

Keywords: curve diffusion, plane curves


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Letzte Änderung: 10.02.2016 - Ansprechpartner: Pierre Krenzlin