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Asymptotic analysis of a class of Ginzburg–Landau equations in thin multidomains

  • Abdellatif Messaoudi EMAIL logo
Published/Copyright: August 11, 2016

Abstract

This paper addresses the asymptotic analysis of minimizers of the classical Ginzburg–Landau energy in a thin multidomain. More precisely we are interested in the minimization of the energy

En,ε(u)=12Ωn|u|2+14ε2Ωn(1-|u|2)2

over all maps u:Ωn, satisfying a partial boundary Dirichlet condition u=g on a specific subset of Ωn. Here Ωn2 is a thin bounded multidomain, and g:S1 is a given smooth map. The analysis is performed in the case where Ωn is made of a thin horizontal plate of vanishing thickness with a “forest” of vertical cylinders on the top of it of vanishing width as n. The main issue addressed here is to determine the behavior of minimizers as n and then ε0, and conversely.

MSC 2010: 35B27; 35Q56; 35B40

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Received: 2015-11-30
Revised: 2016-6-19
Accepted: 2016-6-20
Published Online: 2016-8-11
Published in Print: 2016-10-1

© 2016 by De Gruyter

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