The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature
Abstract
We show by using formal asymptotics that the zero level set of the solution to the Cahn–Hilliard equation with a concentration dependent mobility approximates to lowest order in ɛ. an interface evolving according to the geometric motion, (where V is the normal velocity, Δ8is the surface Laplacian and κ is the mean curvature of the interface), both in the deep quench limit and when the temperature θ is where є 2 is the coefficient of gradient energy. Equation (0.1) may be viewed as motion by surface diffusion, and as a higher-order analogue of motion by mean curvature predicted by the bistable reaction-diffusion equation.
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Citations
Cites
Free Energy of a Nonuniform System. I. Interfacial Free Energy
Cahn, J. W., & Hilliard, J. E. (1958) · The Journal of Chemical Physics · doi:10.1063/1.1744102 · Cited by 10,437
Self-citationInfinite-Dimensional Dynamical Systems in Mechanics and Physics
Temam, R. (1997) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-0645-3 · Cited by 5,396
Allen, S. M., & Cahn, J. W. (1979) · Acta Metallurgica · doi:10.1016/0001-6160(79)90196-2 · Cited by 3,796
Self-citationCahn, J. W. (1961) · Acta Metallurgica · doi:10.1016/0001-6160(61)90182-1 · Cited by 3,588
Self-citationMullins, W. W. (1957) · Journal of Applied Physics · doi:10.1063/1.1722742 · Cited by 2,629 · cited 2×
“5 Conclusion The geometric motion given by minus the surface Laplacian of the curvature has been previously derived by Mullins in the context of surface diffusion for single component alloys in a vapour environment [16] and by Davi & Gurtin [17] in the general thermodynamic framework of [24].”
BackgroundMethodInfinite-Dimensional Dynamical Systems in Mechanics and Physics
Temam, R. (1988) · Applied Mathematical Sciences · doi:10.1007/978-1-4684-0313-8 · Cited by 2,626
The gradient theory of phase transitions and the minimal interface criterion
Modica, L. (1987) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00251230 · Cited by 974
Nonlinear aspects of the Cahn-Hilliard equation
Novick-Cohen, A., & Segel, L. A. (1984) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(84)90180-5 · Cited by 368
Self-citationOverview No. 98 I—Geometric models of crystal growth
Taylor, J. E., Cahn, J. W., & Handwerker, C. A. (1992) · Acta Metallurgica et Materialia · doi:10.1016/0956-7151(92)90090-2 · Cited by 298
Self-citationOverview no. 113 surface motion by surface diffusion
Cahn, J. W., & Taylor, J. E. (1994) · Acta Metallurgica et Materialia · doi:10.1016/0956-7151(94)90123-6 · Cited by 294
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Metadata
- Authors
- Cahn, J. W., Elliott, C. M., & Novick-Cohen, A.
- Venue
- European Journal of Applied Mathematics
- Publisher
- Cambridge University Press (CUP)
- Published
- 1996-06
- Volume
- 7
- Issue
- 3
- Pages
- 287-301
- ISSN
- 0956-7925 (ISSN-L)
- 1469-4425
- OpenAlex
- W1965753687
- Cited by
- 302
- References
- 11
- FWCI
- 6.42
- Type
- journal article
- Language
- en
- Open access
- closed
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- Cahn, J. W., Elliott, C. M., & Novick-Cohen, A. (1996). The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature. European Journal of Applied Mathematics. https://doi.org/10.1017/s0956792500002369
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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