Convergence of phase-field approximations to the Gibbs–Thomson lawReportar como inadecuado




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Calculus of Variations and Partial Differential Equations

, Volume 32, Issue 1, pp 111–136

First Online: 27 October 2007Received: 23 March 2007Accepted: 11 September 2007

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.

Mathematics Subject Classification 2000Primary: 49Q20 Secondary: 35B25 35R35 80A22  Download to read the full article text



Autor: Matthias Röger - Yoshihiro Tonegawa

Fuente: https://link.springer.com/







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