Scaling limits and regularity results for a class of Ginzburg-Landau systems

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 16, Issue 4, 1999, Pages 423-466

  Jerrard, Robert L ^a   Soner, Halil Mete ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013027307     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(99)80024-9     Document Type: Article

References (27)

1. L. AMBROSIO and H.M. SONER, Level set approach to mean curvature flow in arbitrary codimension. J. Diff. Geom., Vol. 43, 1996, pp. 693-737.
2. G. BARLES, H.M. SONER, and P.E. SOUGANIDIS, Front propagation and phase field theory. SIAM J. Cont. Opt., Vol. 31 (2), 1993, pp. 439-469.
3. P. BAUMAN, C.N. CHEN, D. PHILLIPS, and P. Sternberg, Vortex annihilation in nonlinear heat flow for Ginzburg-Landau systems. European J. Appl. Math., Vol. 6(2), 1995, pp. 115-126.
4. F. BETHUEL, H. BREZIS, and F HÉLEIN, Asymptotics for the minimization of a Ginzburg-Landau functional. Calc. Var., Vol. 1, 1993, pp. 123-148.
5. F. BETHUEL, H. BREZIS, and F HÉLEIN, Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994.
6. 2. Archive Rat. Mech. Anal., Vol. 126, 1994, pp. 35-58.
7. X. CHEN, Generation and propagation of the interface for reaction-diffusion equations. Jour. Diff. Equations, Vol. 96, 1992, pp. 116-141.
8. Y. CHEN and M. STRUWE, Existence and partial regularity results for the heat flow for harmonic maps. Math Z., Vol. 201, 1989, pp. 83-103.
9. W. E., Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Physica D, Vol. 77, 1994, pp. 383-404.
10. L.C. EVANS, H.M. SONER, and P.E. SOUGANIDIS, Phase transitions and generalized motion by curvature. Comm. Pure Appl. Math., Vol. 65, 1992, pp. 1097-1123.
11. T. ILMANEN, Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature. J. Diff. Geom., Vol. 38 (2), 1993, pp. 417-461.
12. R.L. JERRARD, Fully nonlinear phase field equations and generalized mean curvature motion. Comm PDE, Vol. 20, 1995, pp. 233-265.
13. R.L. JERRARD, Lower bounds for generalized Ginzburg-Landau functionals, center for Nonlinear Analysis Research Report No. 95-NA-020, 1995.
14. R.L. JERRARD and H.M. SONER, Dynamics of Ginzburg-Landau vortices, Arch. Rat. Mech. Anal., Vol. 142, 1998, pp. 99-125.
15. N.V. KRYLOV and M.V. SAFONOV, A certain property of solutions of parabolic equations with measurable coefficients. Math. USSR Izvestia, Vol. 16 (1), 1981, pp. 151-164.
16. O.A. LADYZHENSKYA, V.A. SOLONNIKOV, and N.N. Uraltseva. Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, RI, 1968.
17. F.H. LIN, Solutions of Ginzburg-Landau equations and critical points of the renormalized energy. Ann. Inst. H. Poincaré Anal. Non Linéaire, Vol. 12 (5), 1995, pp. 599-622.
18. F.H. LIN, Some dynamical properties of Ginzburg-Landau vortices. Comm. Pure Appl. Math., Vol. 49 (4), 1996, pp. 323-359.
19. J.C. NEU, Vortices in complex scalar fields. Physica D, Vol. 43, 1990, pp. 385-406.
20. L.M. PISMEN and J. RUBINSTEIN, Motion of vortex lines in the Ginzburg-Landau model. Physica D, Vol. 47, 1991, pp. 353-360.
21. J. RUBINSTEIN, Self-induced motion of line vortices. Quart. Appl. Math., Vol. 49 (1), 1991, pp. 1-9.
22. R. SCHOEN, Analytic aspects of the harmonic map problem, In S.S. Chern, editor. Seminar on Nonlinear Partial Differential Equations. Springer, Berlin, 1984.
23. H. METE SONER, Motion of a set by the curvature of its boundary. Jour. Diff. Equations, Vol. 101 (2), 1993, pp. 313-372.
24. M. STRUWE, On the evolution of harmonic maps in higher dimensions. J. Diff. Geom., Vol. 28, 1988, pp. 485-502.
25. M. STRUWE. Variational Methods, Springer-Verlag, Berlin, 1990.
26. M. STRUWE, On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions. Diff. and Int. Equations, Vol. 7 (6), 1994, pp. 1613-1624.
27. Y. KURAMOTO, Chemical Waves, Oscillations, and Turbulence, Springer-Verlag, Berlin, 1984.