Dimension reduction and optimality of the uniform state in a Phase-Field-Crystal model involving a higher order functional
Analysis of PDEs
2019-09-04 v1
Abstract
We study a Phase-Field-Crystal model described by a free energy functional involving second order derivatives of the order parameter in a periodic setting and under a fixed mass constraint. We prove a -convergence result in an asymptotic thin-film regime leading to a reduced 2-dimensional model. For the reduced model, we prove necessary and sufficient conditions for the global minimality of the uniform state. We also prove similar results for the Ohta-Kawasaki model.
Keywords
Cite
@article{arxiv.1812.09200,
title = {Dimension reduction and optimality of the uniform state in a Phase-Field-Crystal model involving a higher order functional},
author = {Radu Ignat and Hamdi Zorgati},
journal= {arXiv preprint arXiv:1812.09200},
year = {2019}
}