On sharp interface limits of Allen--Cahn/Cahn--Hilliard variational inequalities

John W. Barrett; Harald Garcke; Robert Nürnberg

doi:10.3934/dcdss.2008.1.1

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2008, Volume 1, Issue 1: 1-14. Doi: 10.3934/dcdss.2008.1.1

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On sharp interface limits of Allen--Cahn/Cahn--Hilliard variational inequalities

1.
Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ
2.
NWF I - Mathematik, Universität Regensburg, 93040 Regensburg

Received: September 2006

Revised: February 2007

Published online: December 2007

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Abstract

Using formally matched asymptotic expansions we identify the sharp interface asymptotic limit of an Allen-Cahn/Cahn-Hilliard system using a novel approach which enables us to handle the case of variational inequalities.

Keywords:

Degenerate Cahn--Hilliard/Allen--Cahn variational inequality,
matched asymptotic expansions,
degenerate parabolic problem.

Mathematics Subject Classification: Primary: 35K65, 49J40, 35C20; Secondary:35Q60.

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