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Mathematics > Analysis of PDEs

arXiv:1812.09200 (math)
[Submitted on 21 Dec 2018]

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

Authors:Radu Ignat (IMT, UPS), Hamdi Zorgati (LEDP)
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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 $\Gamma$-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.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1812.09200 [math.AP]
  (or arXiv:1812.09200v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1812.09200
Related DOI: https://doi.org/10.1007/s00332-019-09573-0

Submission history

From: Hamdi Zorgati [view email] [via CCSD proxy]
[v1] Fri, 21 Dec 2018 15:39:05 UTC (17 KB)
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