The Dynamics of Nucleation for the Cahn–Hilliard Equation

When a constant metastable solution of the Cahn–Hilliard equation is subjected to a spatially localized large-amplitude perturbation, a transition process may be triggered leading to a globally stable stationary solution. In one space dimension, the existence and instability of a third stationary solution with the same mass is proved: A spike-like solution called a canonical nucleus. Within the class of solutions which are even with respect to the center of the spike, it has a one-dimensional unstable manifold. In addition, the process of nucleation by formal arguments using two space scales and two timescales is described. The last stage in the process can be approximated by a nonlinear Stefan free boundary problem.