English

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 Γ\Gamma-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}
}