Numerics and analysis of Cahn–Hilliard critical points

Mathematical Models and Methods in Applied Sciences 2026 Open access

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Authors: Tobias Grafke, Sebastian Scholtes, Alfred Wagner, Maria G. Westdickenberg
DOI: 10.1142/s0218202526500235
Cited by: 0
References: 9

Abstract

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

Fields of Study & Subjects

Nonlinear Partial Differential Equations Advanced Mathematical Modeling in Engineering Stochastic processes and statistical mechanics

Publication details

Journal / source
Mathematical Models and Methods in Applied Sciences
Publisher
World Scientific Pub Co Pte Ltd
Volume
36
Issue
07
Pages
1381–1414
Publication date
13 March 2026
Language
EN