open access

https://hdl.handle.net/2115/33792

Convergence of phase-field approximations to the Gibbs–Thomson law

英語

2008-05

Springer Berlin / Heidelberg

Calculus of Variations and Partial Differential Equations

32(1)

111-136

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.

学術雑誌論文

Accepted Manuscript

The original publication is available at www.springerlink.com

0944-2669

1432-0835

AA10848617