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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.

35K55 Nonlinear parabolic equations
35K25 Higher-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
Full Text: DOI arXiv
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