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The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature

1996; Cambridge University Press; Volume: 7; Issue: 3 Linguagem: Inglês

10.1017/s0956792500002369

1469-4425

John W. Cahn, Charles M. Elliott, Amy Novick-Cohen,

Advanced Mathematical Modeling in Engineering

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, Δ 8 is 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.