Anomalous scaling for 3d Cahn-Hilliard fronts

Abstract

We prove the stability of the one dimensional kink solution of the Cahn-Hilliard equation under d-dimensional perturbations for d > 2. We also establish a novel scaling behavior of the large time asymptotics of the solution. The leading asymptotics of the solution is characterized by a length scale proportional to the cubic root of t instead of the usual square root of t scaling typical to parabolic problems.