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Anomalous scaling for three-dimensional Cahn-Hilliard fronts. (English) Zbl 1078.35049
Summary: We prove the stability of the one-dimensional kink solution of the Cahn-Hilliard equation under $$d$$-dimensional perturbations for $$d \geqslant 3$$. 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 $$t^{1/3}$$ instead of the usual $$t^{1/2}$$ scaling typical to parabolic problems.

##### MSC:
 35K55 Nonlinear parabolic equations 35K25 Higher-order parabolic equations 35B40 Asymptotic behavior of solutions to PDEs