论文标题
各向异性平均曲率流动的漫射划线近似和弱的独特性
Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow
论文作者
论文摘要
本文的目的是导致各向异性平均曲率流作为各向异性Allen-CAHN方程的极限。我们依靠分布式解决方案概念，用于分散和尖锐的接口模型，并使用相对熵方法证明了收敛性，这些方法最近被证明是界面进化问题中的强大工具。在相同的相对熵的情况下，我们证明了弱的唯一性结果，这取决于我们各向异性能量功能的梯度流量校准的构建。
The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen-Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models, and prove convergence using relative entropy methods, which have recently proven to be a powerful tool in interface evolution problems. With the same relative entropy, we prove a weak-strong uniqueness result, which relies on the construction of gradient flow calibrations for our anisotropic energy functionals.
