HUSCAP logo Hokkaido Univ. logo

Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >

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

Files in This Item:
pre840.pdf268.47 kBPDFView/Open
Please use this identifier to cite or link to this item:http://doi.org/10.14943/83990

Title: CONVERGENCE OF PHASE–FIELD APPROXIMATIONS TO THE GIBBS–THOMSON LAW
Authors: ROGER, MATTHIAS Browse this author
TONEGAWA, YOSHIHIRO Browse this author
Keywords: Phase Transitions
Geometric Measure Theory
Singular Perturbations
Cahn–Hilliard Energy
Gibbs–Thomson Law
Block-copolymers
Issue Date: 2007
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 840
Start Page: 1
End Page: 25
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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69649
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

Export metadata:

OAI-PMH ( junii2 , jpcoar )


 

Feedback - Hokkaido University