On the minimizers of the Ginzburg-Landau energy for high kappa : the axially symmetric case

Amandine Aftalion

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 6, page 747-772
  • ISSN: 0294-1449

How to cite

top

Aftalion, Amandine. "On the minimizers of the Ginzburg-Landau energy for high kappa : the axially symmetric case." Annales de l'I.H.P. Analyse non linéaire 16.6 (1999): 747-772. <http://eudml.org/doc/78482>.

@article{Aftalion1999,
author = {Aftalion, Amandine},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Ginzburg-Landau parameter; Ginzburg-Landau energy; asymptotic behaviour for large of minimizers},
language = {eng},
number = {6},
pages = {747-772},
publisher = {Gauthier-Villars},
title = {On the minimizers of the Ginzburg-Landau energy for high kappa : the axially symmetric case},
url = {http://eudml.org/doc/78482},
volume = {16},
year = {1999},
}

TY - JOUR
AU - Aftalion, Amandine
TI - On the minimizers of the Ginzburg-Landau energy for high kappa : the axially symmetric case
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 6
SP - 747
EP - 772
LA - eng
KW - Ginzburg-Landau parameter; Ginzburg-Landau energy; asymptotic behaviour for large of minimizers
UR - http://eudml.org/doc/78482
ER -

References

top
  1. [1] A. Aftalion, On the minimizers of the Ginzburg-Landau energy for high kappa: the one-dimensional case, EJAM, Vol. 8, 1997, pp. 331-345. Zbl0886.34019MR1471596
  2. [2] P. Baumann, D. Phillips and Q. Tang, Stable nucleation for the Ginzburg-Landau system with an applied magnetic field, Preprint, 1996. 
  3. [3] H. Berestycki, A. Bonnet and S.J. Chapman, A semi-elliptic system arising in the theory of superconductivity, Comm. Appl. Nonlinear Anal., Vol. 1, 3, 1994, pp. 1-21. Zbl0866.35030MR1295490
  4. [4] M.S. Berger and Y.Y. Chen, Symmetric Vortices for the Ginzberg-Landau Equations of Superconductivity and the Nonlinear Desingularisation Phenomenon, J. Func. Anal., Vol. 82, 1989, pp. 259-295. Zbl0685.46051MR987294
  5. [5] F. Bethuel, H. Brezis and F. Helein, Ginzburg-Landau Vortices, Birkhäuser, 1994. Zbl0802.35142MR1269538
  6. [6] C. Bolley, Solutions numériques de problèmes de bifurcation, RAIRO Anal. Num., Vol. 14, 1980, pp. 127-147. Zbl0439.65087MR571311
  7. [7] S.J. Chapman, Nucleation of superconductivity in decreasing fields I, Europ. J. Appl. Math., Vol. 5, 1994, pp. 449-468. Zbl0820.35124MR1309734
  8. [8] S.J. Chapman, Nucleation of superconductivity in decreasing fields II, Europ. J. Appl. Math., Vol. 5, 1994, pp. 469-494. Zbl0820.35124MR1309734
  9. [9] S.J. Chapman, A mean-field model of superconducting vortices in three dimensions, SIAM J. Appl. Math., Vol. 55, 1995, pp. 1259-1274. Zbl0836.76014MR1349309
  10. [10] S.J. Chapman, Motion of vortices in type II superconductors, SIAM J. Appl. Math., Vol. 55, 1995, pp. 1275-1296. Zbl0836.76015MR1349310
  11. [11] S.J. Chapman, S.D. Howison and J.R. Ockendon, Macroscopic models of superconductivity, SIAM Review, Vol. 34, 4, 1992, pp. 529-560. Zbl0769.73068MR1193011
  12. [12] Y.Y. Chen, Nonsymmetric vortices for the Ginzberg-Landau equations on the bounded domain, J. Math. Phys., Vol. 30, 1989, pp. 1942-1950. Zbl0697.35117MR1006155
  13. [13] Q. Du, M.D. Gunzburger and J.S. Peterson, Analysis and approximation of the Ginzburg-Landau model of superconductivity, SIAM Review, Vol. 34, 1, 1992, pp. 54-81. Zbl0787.65091MR1156289
  14. [14] C.M. Elliot, H. Matano and Tang Qi, Zeros of a complex Ginzburg-Landau order parameter with applications to superconductivity, Europ. J. Appl. Math., Vol. 5, 1994, pp. 431-448. Zbl0817.35112MR1309733
  15. [15] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer, Berlin, 1983. Zbl0562.35001MR737190
  16. [16] V.L. Ginzburg and L.D. Landau, On the theory of superconductivity, Soviet Phys. JETP, Vol. 20, 1950, p. 1064. 
  17. [17] H.G. Kaper and M.K. Kwong, Uniqueness of non-negative solutions of semilinear elliptic equations, Nonlinear Diffusion Equations and Their Equilibrium States, II, W. M. Ni, L. A. Peletier and J. Serrin (eds.), MSRI Conf. Proc., Springer-Verlag, New York, 1988, pp. 1-17. Zbl0662.35037MR956078

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.