On the slow dynamics for the Cahn–Hilliard equation in one space dimension

We study the limiting behaviour of the solution of the Cahn-Hilliard equation using ‘energy-type methods'. We assume that the initial data has a ‘transition layer structure’, i.e. uϵ ≈ ± 1 except near finitely many transition points. We show that, in the limit as ϵ → 0, the solution maintains its transition layer structure, and the transition layers move slower than any power of ϵ.

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