Open AccessLocal minimizers and slow motion for the mass preserving Allen–Cahn equation in higher dimensions
Author(s) -
Giovanni Leoni,
Ryan Murray
Publication year - 2019
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/13988
Subject(s) - annotation , dimension (graph theory) , algorithm , convergence (economics) , semantics (computer science) , type (biology) , motion (physics) , computer science , artificial intelligence , mathematics , pure mathematics , programming language , geology , paleontology , economics , economic growth
This paper completely resolves the asymptotic development of order 2 2 by Γ \Gamma -convergence of the mass-constrained Cahn–Hilliard functional. Important new results on the slow motion of interfaces for the mass preserving Allen–Cahn equation and the Cahn–Hilliard equations in higher dimension are obtained as an application.