Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow

Tim Laux; Kerrek Stinson; Clemens Ullrich

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arXiv · 2212.11939

Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow

Tim Laux·Kerrek Stinson·Clemens Ullrich

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Abstract

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.

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Tim Laux, Kerrek Stinson, Clemens Ullrich. 2022-12-22. Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow. https://arxiv.org/abs/2212.11939

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