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arXiv · 1209.6531

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

Selim Esedoglu·Andreas Rätz·Matthias Röger
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Abstract

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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Selim Esedoglu, Andreas Rätz, Matthias Röger. 2012-09-28. Colliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow. https://arxiv.org/abs/1209.6531

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