Homogenization and Phase Separation with Fixed Wells -- The Supercritical Case

Irene Fonseca; Likhit Ganedi; Riccardo Cristoferi

Homogenization and Phase Separation with Fixed Wells -- The Supercritical Case

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arxiv 2301.07012 v2 pith:PCDKWVEC submitted 2023-01-17 math.AP

Riccardo Cristoferi , Irene Fonseca , Likhit Ganedi This is my paper · ORCID

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keywords separationhomogenizationphasebeenbradiescaseconjecturedconsidered

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abstract

A variational model for the interaction between homogenization and phase separation is considered in the regime where the former happens at a finer scale than the latter. The first order $\Gamma-$limit is proven to exhibit a separation of scales which has been previously conjectured in a paper by Bradies and Zeppieri and in the PhD thesis of Hagerty.

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Convergence of a heterogeneous Allen-Cahn equation to weighted mean curvature flow
math.AP 2024-12 conditional novelty 6.0 of 10

Under an energy convergence hypothesis, solutions of a heterogeneous Allen-Cahn equation with space-dependent wells converge to a BV solution of weighted mean curvature flow, and a weak-strong uniqueness principle holds.

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