论文标题
Allen-CAHN类型方程的差异的收敛速率
A convergence rate of the discrepancy for Allen-Cahn type equation
论文作者
论文摘要
本文提出了一个新的部分微分方程，以构建Brakke的运动，这是平均曲率流的弱概念。我们称该方程为修改后的Allen-Cahn方程，缩写为Mac。之后，我们介绍了它的好处：对差异能量的改进估计，这意味着第一个能量的焦点。该方程是通过在allen-cahn方程时间依赖于时间依赖的参数并添加类似z transform的术语来获得的。此外，我们提到了通过Mac的动作的存在。
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.
