Anomalous scaling for 3d Cahn-Hilliard fronts

Details Anomalous scaling for 3d Cahn-Hilliard fronts Anomalous scaling for 3d Cahn-Hilliard fronts

2004-02-10

arxiv.org/abs/math-ph/0402026v1

Physics

Mathematical Physics

34 pages, 4 figures

Scientific paper

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.

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