Geodesic
The Ginzburg–Landau energy with a pinning term oscillating faster than the coherence length
Mickaël Dos Santos1 ; Rémy Rodiac2 ; Etienne Sandier3
1Université Clermont Auvergne, Aubière, France
2Université Paris-Saclay, Orsay, France
3Université Paris-Est Créteil Val-de-Marne, Créteil, France
Interfaces and free boundaries, Tome 25 (2023) no. 3, pp. 491-515

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DOI

The aim of this article is to study the magnetic Ginzburg–Landau functional with an oscillating pinning term. We consider here oscillations of the pinning term that are much faster than the coherence length ε>0, which is also the inverse of the Ginzburg–Landau parameter. We study both the case of a periodic potential and of a random stationary ergodic one. We prove that we can reduce the study of the problem to the case where the pinning term is replaced by its average in the periodic case and by its expectation with respect to the random parameter in the random case. In order to do that, we use a decoupling of the energy (detailed in Lassoued and Mironescu’s 1999 paper) that leads us to the study of the convergence of a scalar positive minimizer of the Ginzburg–Landau energy with pinning term and with homogeneous Neumann boundary conditions. We prove uniform convergence of this minimizer towards the mean value of the pinning term by using a blowup argument and a Liouville-type result for non-vanishing entire solutions of the real Ginzburg–Landau/ Allen–Cahn equation, due to the results of Farina (2003).
DOI : 10.4171/ifb/495
Classification : 35-XX
Mots-clés : supraconductivity, Ginzburg–Landau model, pinning, homogenization

Mickaël Dos Santos  1   ; Rémy Rodiac  2   ; Etienne Sandier  3

1 Université Clermont Auvergne, Aubière, France
2 Université Paris-Saclay, Orsay, France
3 Université Paris-Est Créteil Val-de-Marne, Créteil, France 
Mickaël Dos Santos; Rémy Rodiac; Etienne Sandier. The Ginzburg–Landau energy with a pinning term oscillating faster than the coherence length. Interfaces and free boundaries, Tome 25 (2023) no. 3, pp. 491-515. doi: 10.4171/ifb/495
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     title = {The {Ginzburg{\textendash}Landau} energy with a pinning term oscillating faster than the coherence length},
     journal = {Interfaces and free boundaries},
     pages = {491--515},
     year = {2023},
     volume = {25},
     number = {3},
     doi = {10.4171/ifb/495},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/495/}
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