论文标题
Allen-CAHN方程与平均曲率流的收敛速率：基于相对熵的简短证明
Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies
论文作者
论文摘要
假设存在于后者的经典（平滑）解决方案，并且从准备充分的初始数据开始，则我们为Allen-CAHN方程向平均曲率流的收敛速率提供了简短且独立的证明。我们的方法基于相对熵技术。特别是，它不需要线性化的Allen-CAHN操作员进行稳定性分析。由于我们的分析也不依赖于比较原则，因此我们希望它适用于更复杂的方程式和系统。
We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique. In particular, it does not require a stability analysis for the linearized Allen-Cahn operator. As our analysis also does not rely on the comparison principle, we expect it to be applicable to more complex equations and systems.
