A variational approach to the volume-preserving anisotropic mean curvature flow in 2D

TL;DR

This paper presents a variational algorithm for modeling volume-preserving anisotropic mean curvature flow in 2D, demonstrating its effectiveness in proving existence and convergence to solutions.

Contribution

The paper introduces a novel variational algorithm for anisotropic mean curvature flow that guarantees existence and convergence of solutions in 2D.

Findings

Algorithm proves existence of classical solutions.

Algorithm converges to the global solution.

Applicable to volume-preserving anisotropic flows.

Abstract

In this article, we introduce a variational algorithm, in the spirit of the minimizing movements scheme, to model the volume-preserving anisotropic mean curvature flow in 2D. We show that this algorithm can be used to prove the existence of classical solutions. Moreover, we prove that this algorithm converges to the global solution of the equation.