Publication: Cauchy problem for the time-dependent Ginzburg-Landau model of superconductivity
Loading...
Full text at PDC
Publication Date
2000
Authors
Wang, Bixiang
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Cambridge University Press
Citations
Exportar
Abstract
The Cauchy problem for the time-dependent Ginzburg-Landau equations of superconductivity in R-d (d = 2, 3) is investigated in this paper. When d = 2, we show that the Cauchy problem for this model is well posed in L-2. When d = 3, we establish the existence result of solutions for L-3 initial data and the uniqueness result for L-4 initial data.
Description
UCM subjects
Unesco subjects
Keywords
Citation
C. Bolley and B. Helffer. Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak κ -limit. Rev. Math. Phys. 8 (1996), 43–83.
C. Bolley and B. Helffer. Proof of the De Gennes formula for the superheating field in the weak κ -limit. Ann. Inst. H. Poincaré Analyse Non Linéaire 14 (1997), 597–613.
S. J. Chapman, S. D. Howison and J. R. Ockendon. Macroscopic models for superconductivity. SIAM Rev. 34 (1992), 529–560.
Z. M. Chen, K. H. Hoffmann and J. Liang. On a non-stationary Ginzburg-Landau superconductivity model. Math. Meth. Appl. Sci. 16 (1993), 855–875.
Q. Du. Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity. Appl. Analysis 53 (1994), 1–17.
J. Fleckinger-Pellé, H. G. Kaper and P. Takáč. Dynamics of the Ginzburg-Landau equations of superconductivity. Nonlinear Analysis TMA 32 (1998), 647–665.
A. Friedman. Partial differential equations (New York: Holt, Reinhart and Winston, 1969).
L. Gorkov and G. Eliashberg. Generalization of the Ginzburg-Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities. Soviet Phys. JETP 27 (1968), 328–334.
B. Guo and G. Yuan. Cauchy problem for the Ginzburg-Landau equation for the superconductivity model. Proc. R. Soc. Edinb. A 127 (1997), 1181–1192.
J. L. Lions, Quelques Methodes de Resolution des Problems Auxlimites Non Lineaires (Paris: Dunod, 1969).
Q. Tang. On an evolutionary system of Ginzburg-Landau equations with fixed total magnetic flux. Commun. Partial Diff. Eqns 20 (1995), 1–36.
Q. Tang and S. Wang. Time dependent Ginzburg-Landau equations of superconductivity. Physica D 88 (1995), 139–166.
R. Temam. Infinite dimensional dynamical systems in mechanics and physics (Springer, 1988).
B. Wang. Uniqueness of solutions for the Ginzburg-Landau model of superconductivity in three spatial dimensions. J. Math. Analysis Appl. (In the press.)
B. Wang and N. Su. Global weak solutions for the Ginzburg-Landau equations of superconductivity. Appl. Math. Lett. 12 (1999), 115–118.
S. Wang and M. Zhan. L p solutions to the time dependent Ginzburg-Landau equations of superconductivity. Indiana University ISCAM No. 9622. Nonlinear Analysis 36 (1999), 661–677.
Y. Yang. Existence, regularity and asymptotic behaviour of the solutions to the Ginzburg-Landau equations on R 3 . Commun. Math. Phys. 123 (1989), 147–161.
Y. Yang. On the abelian Higgs models with sources. J. Math. Pures Appl. 70 (1991), 325–344.
Y. Yang. The existence of Ginzburg-Landau solutions on the plane by a direct variational method. Ann. Inst. H. Poincaré Analyse Non Linéaire 11 (1994), 517–536.