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

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dc.creatorRöger, M.
dc.creatorTonegawa, Y.
dc.date2007-03-23
dc.date.accessioned2026-07-07T07:53:24Z
dc.date.available2026-07-07T07:53:24Z
dc.descriptionWe 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.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0703689
dc.identifierhttp://arxiv.org/abs/math/0703689
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126243
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subjectPrimary 49Q20; Secondary 35B25, 35R35,80A22
dc.titleConvergence of phase-field approximations to the Gibbs-Thomson law
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