Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model
ESAIM: Modélisation mathématique et analyse numérique, Tome 32 (1998) no. 1, pp. 25-50.
@article{M2AN_1998__32_1_25_0,
     author = {Chen, Zhiming and Elliott, C. M. and Qi, Tang},
     title = {Justification of a two dimensional evolutionary {Ginzburg-Landau} superconductivity model},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {25--50},
     publisher = {Elsevier},
     volume = {32},
     number = {1},
     year = {1998},
     mrnumber = {1619592},
     zbl = {0905.35084},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1998__32_1_25_0/}
}
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: Modélisation mathématique et analyse numérique
PY  - 1998
SP  - 25
EP  - 50
VL  - 32
IS  - 1
PB  - Elsevier
UR  - http://archive.numdam.org/item/M2AN_1998__32_1_25_0/
LA  - en
ID  - M2AN_1998__32_1_25_0
ER  - 
%0 Journal Article
%A Chen, Zhiming
%A Elliott, C. M.
%A Qi, Tang
%T Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1998
%P 25-50
%V 32
%N 1
%I Elsevier
%U http://archive.numdam.org/item/M2AN_1998__32_1_25_0/
%G en
%F M2AN_1998__32_1_25_0
Chen, Zhiming; Elliott, C. M.; Qi, Tang. Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model. ESAIM: Modélisation mathématique et analyse numérique, Tome 32 (1998) no. 1, pp. 25-50. http://archive.numdam.org/item/M2AN_1998__32_1_25_0/

[CHO 92] S. J. Chapman, S. D. Howinson and J. R. Ockendon; Macroscopic models for superconductivity; SIAM Review, 34 (1990), 529-560. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[DG 93] Q. Du and M. D. Gunzburger; A model for superconducting thin films having variable thickness; to appear. | MR | Zbl

[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. | MR | Zbl

[DL 76] G. Duvaut, J. L. Lions; Inequalities in Mechanics and Physics; Springer, 1976. | MR | Zbl

[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. | MR | Zbl

[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.

[G 85] P. Grisvard; Elliptic Problems in Nonsmooth Domains; Pitman, 1985. | MR | Zbl

[GR 86] V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations; Springer-Verlag, 1986. | MR | Zbl

[JT 80] A. Jaffe and C. Taubes, Vortices and Monopoles; Birkhauser, 1980. | MR | Zbl

[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. | MR | Zbl

[Mo 66] C. B. Morrey, Multiple Integrals in the Calculus of Variations; Springer, 1966. | Zbl

[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. | Numdam | MR | Zbl

[Ne 67] J. Necas, Les Méthodes Directes en Théorie des Equations Elliptique; Masson, 1967. | MR

[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. | MR | Zbl

[TW 95] Q. Tang and S. Wang, Time dependent Ginzburg-Landau equations of superconductivity, Physica D, Vol. 8 (1995), 139-166. | MR | Zbl