新旧Willmore流扩散界面近似中的界面碰撞
Colliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow
AI总结：
本文研究Willmore流的扩散界面近似，通过数值实验展示标准模型在界面碰撞时出现角点演化，并提出替代近似以获得更规则的行为，其动力学源于收敛到Willmore能量L1下半连续包络的近似能量。
摘要：
本文关注Willmore流的扩散界面近似。我们首先展示标准扩散界面模型在一维界面碰撞中的数值结果。在这种情形下，可能出现朝向带有角点的界面的演化，这不一定描述适当的尖锐界面动力学。因此，我们提出并研究替代的扩散界面近似，这些近似在界面碰撞时导致不同且更规则的行为。这些动力学源自于近似能量，这些能量收敛到Willmore能量的$L^1$-下半连续包络，而对于更标准的Willmore近似，这一点通常不成立。
英文摘要：
This paper is concerned with diffuse-interface approximations of the Willmore flow. We first present numerical results of standard diffuse-interface models for colliding one dimensional interfaces. In such a scenario evolutions towards interfaces with corners can occur that do not necessarily describe the adequate sharp-interface dynamics. We therefore propose and investigate alternative diffuse-interface approximations that lead to a different and more regular behavior if interfaces collide. These dynamics are derived from approximate energies that converge to the $L^1$-lower-semicontinuous envelope of the Willmore energy, which is in general not true for the more standard Willmore approximation.
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