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.
Cite this article
Carina Geldhauser, Matteo Novaga, A semidiscrete scheme for a one-dimensional Cahn–Hilliard equation. Interfaces Free Bound. 13 (2011), no. 3, pp. 327–339