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

Laux T, Stinson K, Ullrich C (2024)

Publication Type: Journal article

Publication year: 2024

Journal

European Journal of Applied Mathematics Cambridge University Press

DOI: 10.1017/S0956792524000226

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.

Authors with CRIS profile

Clemens Ullrich Professur für Angewandte Mathematik (Analysis und Numerik partieller Differentialgleichungen)

Involved external institutions

Rheinische Friedrich-Wilhelms-Universität Bonn DE Germany (DE) Universität Regensburg DE Germany (DE)

How to cite

APA:

Laux, T., Stinson, K., & Ullrich, C. (2024). Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow. European Journal of Applied Mathematics. https://doi.org/10.1017/S0956792524000226

MLA:

Laux, Tim, Kerrek Stinson, and Clemens Ullrich. "Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow." European Journal of Applied Mathematics (2024).

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