Convergence of phase-field approximations to the Gibbs–Thomson law |
| |
Authors: | Matthias Röger Yoshihiro Tonegawa |
| |
Institution: | (1) Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany;(2) Department of Mathematics, Hokkaido University Sapporo, 060-0810 Sapporo, Japan |
| |
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. |
| |
Keywords: | Primary: 49Q20 Secondary: 35B25 35R35 80A22 |
本文献已被 SpringerLink 等数据库收录! |