Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model

Zhiming Chen; C. M. Elliott; Tang Qi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1998)

  • Volume: 32, Issue: 1, page 25-50
  • ISSN: 0764-583X

How to cite

top

Chen, Zhiming, Elliott, C. M., and Qi, Tang. "Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.1 (1998): 25-50. <http://eudml.org/doc/193866>.

@article{Chen1998,
author = {Chen, Zhiming, Elliott, C. M., Qi, Tang},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {two dimensional evolutionary Ginzburg-Landau superconductivity model; existence of weak solutions; three dimensional variable thickness model},
language = {eng},
number = {1},
pages = {25-50},
publisher = {Dunod},
title = {Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model},
url = {http://eudml.org/doc/193866},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Chen, Zhiming
AU - Elliott, C. M.
AU - Qi, Tang
TI - Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 1
SP - 25
EP - 50
LA - eng
KW - two dimensional evolutionary Ginzburg-Landau superconductivity model; existence of weak solutions; three dimensional variable thickness model
UR - http://eudml.org/doc/193866
ER -

References

top
  1. [CHO 92] S. J. CHAPMAN, S. D. HOWINSON and J. R. OCKENDON; Macroscopic models for superconductivity; SIAM Review, 34 (1990), 529-560. Zbl0769.73068MR1193011
  2. [CH 95] Z. CHEN and K.-F. HOFFMANN; Numerical studies of a non-stationary Ginzburg-Landau model for superconductivity; Adv. Math. Sci. Appl. 5 (1995), 363-389. Zbl0846.65051MR1360996
  3. [CHL 93] Z. CHEN, K. H. HOFFMANN and J. LIANG; On a non-stationary Ginzburg-Landau superconductivity model; Math. Meth. Appl. Sci., 16 (1993), 855-875. Zbl0817.35111MR1247887
  4. [Du 94] Q. DU; Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity; Applicable Analysis 52 (1994), 1-17. Zbl0843.35019MR1379180
  5. [DG 93] Q. DU and M. D. GUNZBURGER; A model for superconducting thin films having variable thickness; to appear. Zbl0794.58049MR1251263
  6. [DGP 92] Q. DU, M. D. GUNZBURGER and J. S. PETERSON; Analysis and approximation of the Ginzburg-Landau model of superconductivity; Siam Review, 34 (1992), 54-81. Zbl0787.65091MR1156289
  7. [DL 76] G. DUVAUT, J. L. LIONS; Inequalities in Mechanics and Physics; Springer, 1976. Zbl0331.35002MR521262
  8. [EMT 93] C. M. ELLIOTT, H. MATANO and Q. TANG; Zeros of a complex Ginzburg-Landau order parameter with applications to superconductivity; Eur. J. Appl. Math., Vol. 5, No 7 (1994), 437-448. Zbl0817.35112MR1309733
  9. [GE 68] L. P. GOR'KOV, G. M ELIASHBERG; Generalisation of the Ginzburg-Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities; Soviet Phys. J.E.T.P., 27 (1968), 328-334. 
  10. [G 85] P. GRISVARD; Elliptic Problems in Nonsmooth Domains; Pitman, 1985. Zbl0695.35060MR775683
  11. [GR 86] V. GIRAULT and P. A. RAVIART, Finite Element Methods for Navier-Stokes Equations; Springer-Verlag, 1986. Zbl0585.65077MR851383
  12. [JT 80] A. JAFFE and C. TAUBES, Vortices and Monopoles; Birkhauser, 1980. Zbl0457.53034MR614447
  13. [LT 93] J. LIANG and Q. TANG, Asymptotic behavior of the solutions of an evolutionary Ginzburg-Landau superconductivity model; J. Math. Anal. Appl., Vol. 195 (1995), 92-107. Zbl0845.35118MR1352812
  14. [Mo 66] C. B. MORREY, Multiple Integrals in the Calculus of Variations; Springer, 1966. Zbl0142.38701
  15. [MTY 93] S. MULLER, Q. TANG and B. S. YAN; On a new class of elastic deformations not allowing for cavitations, Ann. Inst. H. Poincaré, Analyse Non Linear, Vol. 11 (1994), 217-243. Zbl0863.49002MR1267368
  16. [Ne 67] J. NECAS, Les Méthodes Directes en Théorie des Equations Elliptique; Masson, 1967. MR227584
  17. [T 95] Q. TANG, On a evolutionary system of Ginzburg-Landau equations with fixed total magnetic flux; Commun in Partial Differential Equations, 20 (1 and 2) (1995), 1-36. Zbl0833.35132MR1312698
  18. [TW 95] Q. TANG and S. WANG, Time dependent Ginzburg-Landau equations of superconductivity, Physica D, Vol. 8 (1995), 139-166. Zbl0900.35371MR1360881

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.