A convergence rate of the discrepancy for Allen-Cahn type equation
Analysis of PDEs
2022-08-04 v1 Differential Geometry
Abstract
This paper presents a new partial differential equation to build Brakke's motion, which is a weak notion of mean curvature flow. We call the equation a modified Allen-Cahn equation abbreviated to MAC. After that we introduce its benefit: An improved estimate on the discrepant energy that means the equipartition of the first energy. This equation is obtained by rendering the parameter in Allen-Cahn equation time-dependent and adding a term like Z-transform. Furthermore, we mention the existence of a Brakke's motion through our MAC.
Keywords
Cite
@article{arxiv.2208.01775,
title = {A convergence rate of the discrepancy for Allen-Cahn type equation},
author = {Kazuhiro Horihata},
journal= {arXiv preprint arXiv:2208.01775},
year = {2022}
}