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,(whereVis 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 iswhere є2is 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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