Vortex Dynamics of Ginzburg-Landau Equations in Inhomogeneous Superconductors

Journal of Differential Equations

Volumn 170, Issue 1, 2001, Pages 123-141

  Jian, Huai Yu ^a   Song, Bin Heng ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Ginzburg Landau system; vortex pinning; dynamics; parabolic estimate

Indexed keywords

EID: 0041917632     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3822     Document Type: Article

References (16)

1. Chapman S. J., Richardson G. Vortex pinning by inhomogeneities in type-II superconductors. Phys. D. 108:1997;397-407.
2. Chapman S. J., Du Q., Gunzburger M. D. A Ginzburg-Landau type model of superconducting/normal junctions including Josephson junctions. European J. Appl. Math. 6:1995;97-114.
3. Rubinstein J. On the equilibrium position of Ginzburg-Landau vortices. Z. Angew. Math. Phys. 46:1995;739-751.
4. Bethuel T., Brezis H., Hélein F. Ginzburg-Landau Vortices. 1994;Birkhäuser, Boston.
5. Lin F. H. Solutions of Ginzburg-Landau equations and critical points of the renormalized energy. Ann. Inst. H. Poincaré Anal. Non Linéaire. 15:1995;599-622.
6. Struwe M. On the asymptotic behaviour of minimizers of the Ginzburg-Landau model in 2-dimensions. J. Differential Integral Equations. 7:1994;1613-1624.
7. Lin F. H. Some dynamical properties of Ginzburg-Landau vortices, I, II. Comm. Pure Appl. Math. 49:1996;323-364.
8. Jerrard R., Soner H. M. Dynamics of Ginzburg-Landau vortices. Arch. Rat. Mech. 142:1998;99-125.
9. Lin F. H. Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds. Comm. Pure Appl. Math. 51:1998;385-441.
10. Jian H. Y. The dynamical law of Ginzburg-Landau vortices with a pinning effect. Appl. Math. Lett. 13:2000;91-94.
11. Zhang Z. F., Ding T. R. Stability Theorey of Differential Equations. 1997;Science Press, Beijing.
12. Lojasiewicz S. Une propriété topologique des sousensembles analytiques réels. Colloques Internationaux du C.N.R.S. Les Equations Aux Derivées Partielles. 117:1963.
13. Simon L. Asymptotics for a class of non-linear evolution equations with application to geometric problems. Ann. of Math. 118:1983;525-571.
14. Jian H. Y., Wang Y. D. Ginzburg-Landau vortices in inhomogeneous superconductor. Adv. Math. 28:1999;83-84.
15. Giaquinta M. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. 1983;Princeton Univ. Press, Princeton.
16. Gilbarg D., Trudinger N. S. Elliptic Partial Differential Equations of Second Order. 1977;Springer-Verlag, Heidelberg/New York.