We prove the stability of the one-dimensional kink solution of the Cahn-Hilliard equation under d-dimensional perturbations for d ≥ 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.
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