We analyze a semidiscrete scheme for the Cahn–Hilliard equation in one space dimension, when the interface length parameter is equal to zero. We prove convergence of the scheme for a suitable class of initial data, and we identify the limit equation. We also characterize the long-time behavior of the limit solutions.
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Carina Geldhauser, Matteo Novaga, A semidiscrete scheme for a one-dimensional Cahn–Hilliard equation. Interfaces Free Bound. 13 (2011), no. 3, pp. 327–339DOI 10.4171/IFB/260