Energy barrier and \(\Gamma\)-convergence in the \(d\)-dimensional Cahn-Hilliard equation

We study the d-dimensional Cahn-Hilliard equation on the flat torus in a parameter regime in which the system size is large and the mean value is close---but not too close---to -1. We are particularly interested in a quantitative description of the energy landscape in the case in which the uniform s...

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Veröffentlicht in:arXiv.org 2014-12
Hauptverfasser: Gelantalis, Michael, Westdickenberg, Maria G
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Sprache:eng
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Zusammenfassung:We study the d-dimensional Cahn-Hilliard equation on the flat torus in a parameter regime in which the system size is large and the mean value is close---but not too close---to -1. We are particularly interested in a quantitative description of the energy landscape in the case in which the uniform state is a local but not global energy minimizer. In this setting, we derive a sharp leading order estimate of the size of the energy barrier surrounding the uniform state. A sharp interface version of the proof leads to a \(\Gamma\)-limit of the rescaled energy gap between a given function and the uniform state.
ISSN:2331-8422
DOI:10.48550/arxiv.1404.5913