2001 Homogenization of harmonic maps with large number of vortices and applications in superconductivity and superfluidity
Leonid Berlyand, Evgenii Khruslov
Adv. Differential Equations 6(2): 229-256 (2001). DOI: 10.57262/ade/1357141494


We study a nonlinear homogenization problem of harmonic maps which describes an ideal superconducting or an ideal superfluid medium with a large number of vortices and the degree conditions prescribed at the external insulating boundary. We derive the homogenized problem which describes the limiting behavior of the fluxes when the total number of vortices tends to infinity. The homogenized problem is described in terms of the effective vorticity and the effective anisotropy tensor. The calculation of this tensor amounts to solving a linear cell problem, which is well studied in the homogenization literature and can be solved by using existing numerical packages. The convergence of the fluxes is rigorously proved. We also discuss unusual features of the homogenized limit for the wave functions. The proofs are based on a variational approach which does not require periodicity and can be used in more general situations.


Download Citation

Leonid Berlyand. Evgenii Khruslov. "Homogenization of harmonic maps with large number of vortices and applications in superconductivity and superfluidity." Adv. Differential Equations 6 (2) 229 - 256, 2001. https://doi.org/10.57262/ade/1357141494


Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1142.35330
MathSciNet: MR1799751
Digital Object Identifier: 10.57262/ade/1357141494

Primary: 35B27
Secondary: 35J60 , 58E20 , 82D50 , 82D55

Rights: Copyright © 2001 Khayyam Publishing, Inc.


This article is only available to subscribers.
It is not available for individual sale.

Vol.6 • No. 2 • 2001
Back to Top