Bates, Peter W.; Xun, Jianping Metastable patterns for the Cahn-Hilliard equation. I. (English) Zbl 0805.35046 J. Differ. Equations 111, No. 2, 421-457 (1994). 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 \(c>0\). Reviewer: M.Fila (Bratislava) Cited in 3 ReviewsCited in 35 Documents MSC: 35K35 Initial-boundary value problems for higher-order parabolic equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:slow evolution; one-dimensional Cahn-Hilliard equation; global unstable manifold PDFBibTeX XMLCite \textit{P. W. Bates} and \textit{J. Xun}, J. Differ. Equations 111, No. 2, 421--457 (1994; Zbl 0805.35046) Full Text: DOI