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

Michael Gelantalis; Maria G. Westdickenberg

doi:10.1007/s00526-014-0806-x

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arXiv · 1404.5913

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

Michael Gelantalis·Maria G. Westdickenberg

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Abstract

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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Michael Gelantalis, Maria G. Westdickenberg. 2014-04-23. Energy barrier and $\Gamma$-convergence in the $d$-dimensional Cahn-Hilliard equation. https://doi.org/10.1007/s00526-014-0806-x

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