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March  2008, 1(1): 1-14. doi: 10.3934/dcdss.2008.1.1

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

John W. Barrett 1, , Harald Garcke 2, and  Robert Nürnberg 1,

1. 

Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom, United Kingdom
2. 

NWF I - Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Received  September 2006 Revised  February 2007 Published  December 2007

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: matched asymptotic expansions, Degenerate Cahn--Hilliard/Allen--Cahn variational inequality, degenerate parabolic problem..
Mathematics Subject Classification: Primary: 35K65, 49J40, 35C20; Secondary:35Q6.
Citation: John W. Barrett, Harald Garcke, Robert Nürnberg. On sharp interface limits of Allen--Cahn/Cahn--Hilliard variational inequalities. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 1-14. doi: 10.3934/dcdss.2008.1.1
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