A semidiscrete scheme for a one-dimensional Cahn–Hilliard equation

Carina Geldhauser, Matteo Novaga
2011 Interfaces and free boundaries (Print)  
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. keywords: Nonconvex functionals, forward-backward parabolic equations, finite element method.
doi:10.4171/ifb/260 fatcat:u3izpke5d5a4nbw7bhksj4rtau