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 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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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. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.1404.5913 |