The Cahn-Hilliard equation as degenerate limit of the phase-field equations
Author:
Barbara E. E. Stoth
Journal:
Quart. Appl. Math. 53 (1995), 695-700
MSC:
Primary 35Q99; Secondary 35K55, 80A22, 82B26
DOI:
https://doi.org/10.1090/qam/1359505
MathSciNet review:
MR1359505
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We show that the Cahn-Hilliard equation occurs as a special scaling limit of the phase-field equation.
G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rat. Mech. Anal. 92, 205–245 (1986)
G. Caginalp, Stefan and Hele Shaw type models as asymptotic limits of the phase-field equations, Physical Review A39, No. 11, 5887–5896 (1989)
C. M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, Mathematical models for phase change problems, Proc. European Workshop, Obidos/Port. 1989, Internat. Ser. Numer. Math. 88, 35–73 (1989)
C. M. Elliott and S. Zheng, On the Cahn-Hilliard equation, Arch. Rat. Mech. Anal. 96, 339–357 (1986)
C. M. Elliott and S. Zheng, Global Existence and Stability of Solutions to the Phase Field Equations, SFB 256–Report No. 74, Bonn, 1989
St. Luckhaus, Solutions of the two phase Stefan problem with the Gibbs-Thomson law for the melting temperature, European J. Appl. Math. 1, 101–111 (1990)
G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rat. Mech. Anal. 92, 205–245 (1986)
G. Caginalp, Stefan and Hele Shaw type models as asymptotic limits of the phase-field equations, Physical Review A39, No. 11, 5887–5896 (1989)
C. M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, Mathematical models for phase change problems, Proc. European Workshop, Obidos/Port. 1989, Internat. Ser. Numer. Math. 88, 35–73 (1989)
C. M. Elliott and S. Zheng, On the Cahn-Hilliard equation, Arch. Rat. Mech. Anal. 96, 339–357 (1986)
C. M. Elliott and S. Zheng, Global Existence and Stability of Solutions to the Phase Field Equations, SFB 256–Report No. 74, Bonn, 1989
St. Luckhaus, Solutions of the two phase Stefan problem with the Gibbs-Thomson law for the melting temperature, European J. Appl. Math. 1, 101–111 (1990)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
35Q99,
35K55,
80A22,
82B26
Retrieve articles in all journals
with MSC:
35Q99,
35K55,
80A22,
82B26
Additional Information
Article copyright:
© Copyright 1995
American Mathematical Society
