Calculus of Variations and Partial Differential Equations
巻, 号, ページ
Vol. 32
No. 1
p. 111-136
出版年月
2008年
出版者
和文:
英文:
Springer Berlin / Heidelberg
会議名称
和文:
英文:
開催地
和文:
英文:
アブストラクト
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.
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