The p-elastic flow for planar closed curves with constant parametrization

Authors

Shinya Okabe, Tohoku University
Glen Wheeler, University of Wollongong

Publication Name

Journal des Mathematiques Pures et Appliquees

Abstract

In this paper, we consider the L2-gradient flow for the modified p-elastic energy defined on planar closed curves. We formulate a notion of weak solution for the flow and prove the existence of global-in-time weak solutions with p≥2 for initial curves in the energy space via minimizing movements. Moreover, we prove the existence of unique global-in-time solutions to the flow with p=2 and obtain their subconvergence to an elastica as t→∞.

Open Access Status

This publication may be available as open access

Volume

173

First Page

1

Last Page

42

Funding Number

JP19H05599

Funding Sponsor

Japan Society for the Promotion of Science