Dimension Reduction and Optimality of the Uniform State in a Phase-Field-Crystal Model Involving a Higher-Order Functional |
| |
Authors: | Radu Ignat Hamdi Zorgati |
| |
Institution: | 1.Institut de Mathématiques de Toulouse & Institut Universitaire de France, UMR 5219, Université de Toulouse, CNRS, UPS IMT, 31062, Toulouse Cedex 9, France;2.Département de Mathématiques, Faculté des Sciences de Tunis, Université Tunis El Manar, 2092, Tunis, Tunisia |
| |
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 $$\Gamma $$-convergence result in an asymptotic thin-film regime leading to a reduced two-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: | |
本文献已被 SpringerLink 等数据库收录! |
|