Energy barrier and $\Gamma$-convergence in the $d$-dimensional Cahn-Hilliard equation
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 -limit of the rescaled energy gap between a given function and the uniform state.
Keywords
Cite
@article{arxiv.1404.5913,
title = {Energy barrier and $\Gamma$-convergence in the $d$-dimensional Cahn-Hilliard equation},
author = {Michael Gelantalis and Maria G. Westdickenberg},
journal= {arXiv preprint arXiv:1404.5913},
year = {2014}
}
Comments
Some very minor changes to the text. Version appearing in Calculus of Variations and Partial Differential Equations. The final publication is available at http://link.springer.com/article/10.1007/s00526-014-0806-x