Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems | Zendy

Rustum Choksi | Zendy; Peter Sternberg | Zendy

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Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems

Author(s) -

Rustum Choksi,

Peter Sternberg

Publication year - 2006

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/148

Subject(s) - isoperimetric inequality , mathematics , cahn–hilliard equation , torus , mean curvature , constant (computer programming) , mathematical analysis , convergence (economics) , curvature , minification , mathematical optimization , geometry , computer science , differential equation , economic growth , economics , programming language

separation: the isoperimetric problem and minimization of the Cahn-Hilliard energy. The two problems are related through a classical result in -convergence and we explore the behavior of global and local minimizers for these problems in the periodic setting. More precisely, we investigate these variational problems for competitors defined on the flat 2- or 3-torus. We view these two problems as prototypes for periodic phase separation. We give a complete analysis of stable critical points of the 2-d periodic isoperimetric problem and also obtain stable solutions to the 2-d and 3-d periodic Cahn-Hilliard problem. We also discuss some intriguing open questions regarding triply periodic constant mean curvature surfaces in 3-d and possible counterparts in the Cahn-Hilliard setting.

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