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2000 A singular limit for a system of degenerate Cahn-Hilliard equations
Harald Garcke, Amy Novick-Cohen
Adv. Differential Equations 5(4-6): 401-434 (2000). DOI: 10.57262/ade/1356651336


A singular limit is considered for a system of Cahn-Hilliard equations with a degenerate mobility matrix near the deep quench limit. Via formal asymptotics, this singular limit is seen to give rise to geometric motion in which the interfaces between the various pure phases move by motion by minus the surface Laplacian of mean curvature. These interfaces may couple at triple junctions whose evolution is prescribed by Young's law, balance of fluxes, and continuity of the chemical potentials. Short time existence and uniqueness is proven for this limiting geometric motion in the parabolic Hölder space ${ C}_{t, \, p}^{1 + \frac{\alpha}{4}, \, 4 + \alpha}, \, 0 <\alpha < 1$, via parameterization of the interfaces.


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Harald Garcke. Amy Novick-Cohen. "A singular limit for a system of degenerate Cahn-Hilliard equations." Adv. Differential Equations 5 (4-6) 401 - 434, 2000.


Published: 2000
First available in Project Euclid: 27 December 2012

zbMATH: 0988.35019
MathSciNet: MR1750107
Digital Object Identifier: 10.57262/ade/1356651336

Primary: 35K65
Secondary: 35K40 , 74A15 , 74N99 , 82C24

Rights: Copyright © 2000 Khayyam Publishing, Inc.


Vol.5 • No. 4-6 • 2000
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