Dept. Math, Hokkaido Univ. EPrints Server

CONVERGENCE OF PHASE–FIELD APPROXIMATIONS TO THE GIBBS–THOMSON LAW

Preprint Series # 840
ROGER, MATTHIAS and TONEGAWA, YOSHIHIRO CONVERGENCE OF PHASE–FIELD APPROXIMATIONS TO THE GIBBS–THOMSON LAW. (2007);

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Abstract

We prove the convergence of phase-field approximations of the Gibbs–Thomson law. This establishes a relation between the first variation of the Van-der-Waals–Cahn–Hilliard energy and the first variation of the area functional. We allow for folding of diffuse interfaces in the limit and the occurrence of higher-multiplicities of the limit energy measures. We show that the multiplicity does not affect the Gibbs–Thomson law and that the mean curvature vanishes where diffuse interfaces have collided. We apply our results to prove the convergence of stationary points of the Cahn–Hilliard equation to constant mean curvature surfaces and the convergence of stationary points of an energy functional that was proposed by Ohta– Kawasaki as a model for micro-phase separation in block-copolymers.

Item Type:Preprint
Subjects:49-xx CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION
ID Code:1692