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

ROGER, MATTHIAS; TONEGAWA, YOSHIHIRO

Hokkaido University Preprint Series in Mathematics, 2007, 840, 1-25

Permalink : https://doi.org/10.14943/83990

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DOI	https://doi.org/10.14943/83990
URI	https://hdl.handle.net/2115/69649
タイトル	CONVERGENCE OF PHASE–FIELD APPROXIMATIONS TO THE GIBBS–THOMSON LAW
著者	著者名 ROGER, MATTHIAS
著者	著者名 TONEGAWA, YOSHIHIRO
言語	英語
キーワード	Phase Transitions
	Geometric Measure Theory
	Singular Perturbations
	Cahn–Hilliard Energy
	Gibbs–Thomson Law
	Block-copolymers
発行日	2007
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	840
ページ	1-25
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record