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Colliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow

机译:Willmore-flow的新旧扩散接口近似中的碰撞接口

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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 L1-lower-semicontinuous envelope of the Willmore energy, which is in general not true for the more standard Willmore approximation.
机译:本文与Willmore流的扩散界面近似有关。我们首先提出用于碰撞一维界面的标准扩散界面模型的数值结果。在这种情况下,可能会发生朝向带有角的界面的演变,而不一定描述足够的尖锐界面动力学。因此,我们提出并研究了替代的扩散界面逼近,如果界面发生碰撞,它们会导致不同且更规则的行为。这些动力学来自会聚到Willmore能量的L1下半连续包络的近似能量,通常对于更标准的Willmore逼近而言,情况并非如此。

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