Existence of time periodic solutions for the Ginzburg-Landau equations of superconductivity

Journal of Mathematical Analysis and Applications

Volumn 232, Issue 2, 1999, Pages 394-412

  Wang, Bixiang ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Superconductivity; existence; Ginzburg Landau equations; periodic solution

Indexed keywords

EID: 0002085627     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1999.6283     Document Type: Article

References (17)

1. Gor'kov L., Eliashberg G. Generalization of the Ginzburg-Landau equations for nonstationary problems in the case of alloys with paramagnetic impurities. Soviet Phys. JETP. 27:1968;328-334.
2. Frahm H., Ullah S., Dorsey A. Flux dynamics and the growth of the superconducting phase. Phys. Rev. Lett. 66:1991;3067-3072.
3. Machida M., Kaburaki H. Direct simulation of the time-dependent Ginzburg-Landau equation for type-II superconducting thin film: vortex dynamics and V-I characteristics. Phys. Rev. Lett. 71:1993;3206-3209.
4. Chapman S. J., Howison S. D., Ockendon J. R. Macroscopic models of superconductivity. SIAM Rev. 34:1992;529-560.
5. Weinan E. Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Phys. D. 77:1994;383-404.
6. Tinkham M. Introduction to Superconductivity. 1975;McGraw-Hill, New York.
7. psolutions to the time dependence Ginzburg-Landau equations of superconductivity, The Institute for Scientific Computing and Applied Mathematics, Indiana University.
8. Chen Z. M., Hoffmann K. H., Liang J. On a non-stationary Ginzburg-Landau superconductivity model. Math. Meth. Appl. Sci. 16:1993;855-875.
9. Du Q. Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity. Appl. Anal. 53:1994;1-17.
10. Tang Q. On an evolutionary system of Ginzburg-Landau equations with fixed total magnetic flux. Comm. Partial Differential Equations. 20:1995;1-36.
11. Tang Q., Wang S. Time dependent Ginzburg-Landau equations of superconductivity. Physica D. 88:1995;139-166.
12. Kaper H. G., Wang B., Wang S. Determining nodes for the Ginzburg-Landau equations of superconductivity. Discrete Continuous Dynamical Systems. 4:1998;205-224.
13. Wang B., Su N. Global weak solutions for the Ginzburg-Landau equations of superconductivity. Appl. Math. Lett. 12:1999;115-118.
14. Adams R. A. Sobolev Spaces. 1975;Academic Press, New York.
15. Girault V., Raviart P. A. Finite Element Methods for Navier-Stokes Equations. 1986;Springer-Verlag, New York.
16. Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. 1988;Springer-Verlag, New York.
17. Amann H. Ordinary Differential Equations: An Introduction to Nonlinear Analysis. 1990;Walter de Gruyter, Berlin.