Long-time stabilization of solutions to the Ginzburg-Landau equations of superconductivity

Monatshefte fur Mathematik

Volumn 133, Issue 3, 2001, Pages 197-221

  Feireisl, Eduard ^a   Takáč, Peter ^b  

^a INSTITUTE OF MATHEMATICS   (Czech Republic)

^b UNIVERSITY OF ROSTOCK   (Germany)

Author keywords

Asymptotically autonomous dynamical process; Gauge; Ginzburg Landau equations; Global attractor; Stabilization; Superconductivity

Indexed keywords

EID: 0037569398     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006050170020     Document Type: Article

References (33)

1. Abrikosov AA (1988) Fundamentals of the Theory of Metals. Amsterdam: North-Holland
2. Adams RA (1975) Sobolev Spaces. New York: Academic Press
3. Chen ZM, Hoffmann K-H, Liang J (1993) On a nonstationary Ginzburg-Landau superconductivity model. Math Methods Appl Sci 16: 855-875
4. DeGennes P (1966) Superconductivity in Metals and Alloys. New York: Benjamin
5. Deimling K (1985) Nonlinear Functional Analysis. Berlin Heidelberg New York: Springer
6. Du Q (1994) Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity. Applicable Anal 53: 1-18
7. Elliott CM, Tang Q (1992) Existence theorems for an evolutionary superconductivity model. Preprint, University of Sussex, Brighton, UK
8. Feireisl E, Simondon F (1996) Convergence for degenerate parabolic equations in one space dimension. CR Acad Sci Paris, Sér I 323: 251-255
9. Feireisl E, Simondon F (1999) Convergence for semilinear degenerate parabolic equations in several space dimensions. J Dynamics Diff Eqs (to appear)
10. Fleckinger Pellé J, Kaper HG (1996) Gauges for the Ginzburg-Landau equations of superconductivity (in: Proceedings of ICIAM'95). Z Angew Math Mech 76(S2): 345-348
11. Fleckinger Pellé J, Kaper HG, Takáč P (1998) Dynamics of the Ginzburg-Landau equations of superconductivity. Nonlin Anal 32: 647-665
12. Georgescu V (1979) Some boundary value problems for differential forms on compact Riemannian manifolds. Ann Mat Pura Appl (4) 122: 159-198
13. Ginzburg VL, Landau LD (1950) On the theory of superconductivity. Zh Eksp Teor Fiz (USSR) 20: 1064-1082; English translation in: D ter Haar, LD Landau (eds) (1965) Men of Physics, Vol I, Oxford: Pergamon Press, pp 138-167
14. Ginzburg VL, Landau LD (1950) On the theory of superconductivity. Zh Eksp Teor Fiz (USSR) 20: 1064-1082; English translation in: D ter Haar, LD Landau (eds) (1965) Men of Physics, Vol I, Oxford: Pergamon Press, pp 138-167
15. Girault V, Raviart P-A (1986) Finite Element Methods for Navier-Stokes Equations. New York: Springer
16. Gor'kov LP, Eliashberg GM (1968) Generalizations of the Ginzburg-Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities. Zh Eksp Teor Fiz 54: 612-626; Soviet Phys JETP 27: 328-334 (1968)
17. Gor'kov LP, Eliashberg GM (1968) Generalizations of the Ginzburg-Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities. Zh Eksp Teor Fiz 54: 612-626; Soviet Phys JETP 27: 328-334 (1968)
18. Hale JK (1988) Asymptotic Behavior of Dissipative Systems. Providence, RI: Amer Math Soc
19. Henry D (1981) Geometric Theory of Semilinear Parabolic Equations. Lect Notes Math 840: Berlin Heidelberg New York: Springer
20. Hoffmann K-H, Rybka P (1998) Convergence of solutions to the equation of quasi-static approximation of viscoelasticity with capillarity. J Math Anal Appl 226: 61-81
21. Jendoubi MA (1998) A simple unified approach to some convergence theorems of L Simon. J Functional Anal 153: 197-202
22. Kaper HG, Takáč P (1997) An equivalence relation for the Ginzburg-Landau equations of superconductivity. Z angew Math Phys (J Appl Math Phys) 48: 665-675
23. Kaper HG, Takáĉ P (1998) Ginzburg-Landau dynamics with a time-dependent magnetic field. Nonlinearity 11: 291-305
24. Liang J, Tang Q (1995) Asymptotic behavior of the solutions of an evolutionary Ginzburg-Landau superconductivity model. J Math Anal Appl 195: 92-107
25. Lin F-H, Du Q (1997) Ginzburg-Landau vortices: dynamics, pinning, and hysteresis. SIAM J Math Anal 28: 1265-1293
26. Lojasiewicz S (1963) Une propriété topologique des sous-ensembles analytiques réels. Colloques internationaux du CNRS #117. Les équationes aux dérivées partielles
27. Rybka P, Hoffmann K-H (1999) Convergence of solutions to the Cahn-Hilliard equation. Comm Partial Differ Eqns 24: 1055-1077
28. Schmid A (1966) A time dependent Ginzburg-Landau equation and its application to the problem of resistivity in the mixed state. Phys Kondens Mater 5: 302-317
29. Simon L (1983) Asymptotics for a class of non-linear evolution equations, with applications to geometric problems. Ann of Math 118: 525-571
30. Takáč P (1996) On the dynamical process generated by a superconductivity model (in: Proceedings of ICIAM'95). Z Angew Math Mech 76 (S2): 349-352
31. Tang Q (1995) On an evolutionary system of Ginzburg-Landau equations with fixed total magnetic flux. Comm Partial Differ Eqns 20: 1-36
32. Tang Q, Wang S (1995) Time dependent Ginzburg-Landau equations of superconductivity. Physica D 88: 139-166
33. Tinkham M (1996) Introduction to Superconductivity, 2nd edn. New York: McGraw-Hill