Advances in Differential Equations

A singular limit for a system of degenerate Cahn-Hilliard equations

Harald Garcke and Amy Novick-Cohen

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Abstract

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.

Article information

Source
Adv. Differential Equations Volume 5, Number 4-6 (2000), 401-434.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651336

Mathematical Reviews number (MathSciNet)
MR1750107

Zentralblatt MATH identifier
0988.35019

Subjects
Primary: 35K65: Degenerate parabolic equations
Secondary: 35K40: Second-order parabolic systems 74A15: Thermodynamics 74N99: None of the above, but in this section 82C24: Interface problems; diffusion-limited aggregation

Citation

Garcke, Harald; Novick-Cohen, Amy. A singular limit for a system of degenerate Cahn-Hilliard equations. Adv. Differential Equations 5 (2000), no. 4-6, 401--434. https://projecteuclid.org/euclid.ade/1356651336.


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