The Cahn-Hilliard model for the kinetics of phase separation. (English) Zbl 0692.73003

Elliott, C. M.

Mathematical models for phase change problems, Proc. Eur. Workshop, Óbidos/Port. 1988, ISNM, Int. Ser. Numer. Math. 88, 35-73 (1989).

[For the entire collection see Zbl 0676.00021.]
The phenomenological theory describing the Cahn-Hilliard mathematical continuum model of phase separation of a binary alloy is presented and the Cahn-Hilliard equations governing the behaviour of this model is derived. Section 2 of the paper contains the existence theory of Cahn- Hilliard’s equation. Some special aspects and generalizations of this equation, the finite element approximation of its solution, and the numerical simulations in some particular cases are surveyed in the Sections 3,4, and 5 of the paper.
This paper is of real interest for physists and mathematicians.

Reviewer: Gh.Gr.Ciobanu

MSC:

74A15	Thermodynamics in solid mechanics
35R60	PDEs with randomness, stochastic partial differential equations
82B26	Phase transitions (general) in equilibrium statistical mechanics
74C15	Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20	Large-strain, rate-dependent theories of plasticity
35A15	Variational methods applied to PDEs
74S05	Finite element methods applied to problems in solid mechanics

Keywords:

spinodal decomposition; finite element approximation; fully discrete schemes; numerical simulations; Lyapunov functionals; binary alloy; Cahn- Hilliard equations; existence theory

Citations:

Zbl 0676.00021