Anomalous scaling for 3d Cahn-Hilliard fronts

2004/02/10 by Timo Korvola, A. Kupiainen, Korvola, Timo +4 · 1 citation
Earth and Planetary Sciences · Materials Science · Mathematics · Physics and Astronomy · #35B40 #35K55 #FOS: Physical sciences #Mathematical Physics (math-ph) #Solidification and crystal growth phenomena #Theoretical and Computational Physics #math-ph #math.MP #msc:35B40 #msc:35K55 #nanoparticles nucleation surface interactions

paper · pdf · doi:10.48550/arxiv.math-ph/0402026

34 pages, 4 figures

arxiv created 2004/02/10 · openalex publication_date 2004/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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