Keywords

Cahn-Hilliard equation, phase separation, transition layers, metastability

Abstract

In this paper we study one-dimensional Cahn-Morral systems, which are the multicomponent analogues of the Cahn-Hilliard model for phase separation and coarsening in binary mixtures. In particular, we examine solutions that start with initial data close to the preferred phases except at finitely many transition points where the data has sharp transition layers, and we show that such solutions may evolve exponentially slowly; i.e., if ε is the interaction length then there exists a constant C such that in exp(C/ε) units of time the change in such a solution is o(1). This corresponds to extremely slow coarsening of a multicomponent mixture after it has undergone fine-grained decomposition.

Original Publication Citation

SIAM Journal on Mathematical Analysis 26.1 (1995), pp. 21-34.