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Metastable patterns for the Cahn-Hilliard equation. I. (English) Zbl 0805.35046

The dynamics of the one-dimensional Cahn-Hilliard equation is studied. A global manifold which is close to being the global unstable manifold of an equilibrium having \(N+1\) interior layers is described and it is shown that a small tubular neighborhood of this manifold attracts nearby points exponentially and points within the neighborhood move with a speed which is \(O(e^{-c/ \varepsilon})\) for some \(c>0\).

MSC:

35K35 Initial-boundary value problems for higher-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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