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arXiv · 1812.09200

Dimension reduction and optimality of the uniform state in a Phase-Field-Crystal model involving a higher order functional

Radu Ignat·Hamdi Zorgati
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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 $Γ$-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.

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Radu Ignat, Hamdi Zorgati. 2018-12-21. Dimension reduction and optimality of the uniform state in a Phase-Field-Crystal model involving a higher order functional. https://doi.org/10.1007/s00332-019-09573-0

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