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Anomalous scaling for 3d Cahn-Hilliard fronts

Timo Korvola·Antti Kupiainen·Jari Taskinen
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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.

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Timo Korvola, Antti Kupiainen, Jari Taskinen. 2004-02-10. Anomalous scaling for 3d Cahn-Hilliard fronts. https://arxiv.org/abs/math-ph/0402026

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