Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow
Analysis of PDEs
2022-12-23 v1
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.
Cite
@article{arxiv.2212.11939,
title = {Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow},
author = {Tim Laux and Kerrek Stinson and Clemens Ullrich},
journal= {arXiv preprint arXiv:2212.11939},
year = {2022}
}