Convergence to equilibrium of gradient flows defined on planar curves
Analysis of PDEs
2013-06-07 v1
Abstract
We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, under different boundary conditions. We prove that, if any set of stationary solutions with fixed energy is finite, then a solution of the flow converges to a stationary solution as time goes to infinity. We also present a few applications of this result.
Cite
@article{arxiv.1306.1406,
title = {Convergence to equilibrium of gradient flows defined on planar curves},
author = {Matteo Novaga and Shinya Okabe},
journal= {arXiv preprint arXiv:1306.1406},
year = {2013}
}