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arXiv · 2104.03689

Numerics and analysis of Cahn--Hilliard critical points

Tobias Grafke·Sebastian Scholtes·Alfred Wagner·Maria G. Westdickenberg
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Abstract

We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in $d\geq 2$ and the critical parameter regime of large system size and mean value close to $-1$. We employ the String Method of E, Ren, and Vanden-Eijnden -- a numerical algorithm for computing transition pathways in complex systems -- in $d=2$ to gain additional insight into the properties of the minima and saddle point. Motivated by the numerical observations, we adapt a method of Caffarelli and Spruck to study convexity of level sets in $d\geq 2$.

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Tobias Grafke, Sebastian Scholtes, Alfred Wagner, Maria G. Westdickenberg. 2021-04-08. Numerics and analysis of Cahn--Hilliard critical points. https://arxiv.org/abs/2104.03689

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