Scaling limits and regularity results for a class of Ginzburg-Landau systems
Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) no. 4, pp. 423-466. 
@article{AIHPC_1999__16_4_423_0,
     author = {Jerrard, Robert L. and Soner, Halil Mete},
     title = {Scaling limits and regularity results for a class of {Ginzburg-Landau} systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {423--466},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {4},
     year = {1999},
     mrnumber = {1697561},
     zbl = {0944.35006},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1999__16_4_423_0/}
}
TY  - JOUR
AU  - Jerrard, Robert L.
AU  - Soner, Halil Mete
TI  - Scaling limits and regularity results for a class of Ginzburg-Landau systems
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1999
SP  - 423
EP  - 466
VL  - 16
IS  - 4
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1999__16_4_423_0/
LA  - en
ID  - AIHPC_1999__16_4_423_0
ER  - 
%0 Journal Article
%A Jerrard, Robert L.
%A Soner, Halil Mete
%T Scaling limits and regularity results for a class of Ginzburg-Landau systems
%J Annales de l'I.H.P. Analyse non linéaire
%D 1999
%P 423-466
%V 16
%N 4
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1999__16_4_423_0/
%G en
%F AIHPC_1999__16_4_423_0
Jerrard, Robert L.; Soner, Halil Mete. Scaling limits and regularity results for a class of Ginzburg-Landau systems. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) no. 4, pp. 423-466. http://www.numdam.org/item/AIHPC_1999__16_4_423_0/

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[5] F. Bethuel, H. Brezis, F. Hélein,Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994. | MR | Zbl

[6] H. Brezis, F. Merle, and T. Riviere, Quantization effects for -Δu = u(1 - |u|2) in R2. Archive Rat. Mech. Anal., Vol. 126, 1994, pp. 35-58. | MR | Zbl

[7] X. Chen, Generation and propagation of the interface for reaction-diffusion equations. Jour. Diff. Equations, Vol. 96, 1992, pp. 116-141. | MR | Zbl

[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. | EuDML | MR | Zbl

[9] W.E., Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Physica D, Vol. 77, 1994, pp. 383-404. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[12] R.L. Jerrard, Fully nonlinear phase field equations and generalized mean curvature motion. Comm PDE, Vol. 20, 1995, pp. 233-265. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[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. | Numdam | MR | Zbl

[18] F.H. Lin, Some dynamical properties of Ginzburg-Landau vortices. Comm. Pure Appl. Math., Vol. 49 (4), 1996, pp. 323-359. | MR | Zbl

[19] J.C. Neu, Vortices in complex scalar fields. Physica D, Vol. 43, 1990, pp. 385-406. | MR | Zbl

[20] L.M. Pismen and J. Rubinstein, Motion of vortex lines in the Ginzburg-Landau model. Physica D, Vol. 47, 1991, pp. 353-360. | MR | Zbl

[21] J. Rubinstein, Self-induced motion of line vortices. Quart. Appl. Math., Vol. 49 (1), 1991, pp. 1-9. | MR | Zbl

[22] R. Schoen, Analytic aspects of the harmonic map problem, In S.S. Chern, editor, Seminar on Nonlinear Partial Differential Equations. Springer, Berlin, 1984. | MR | Zbl

[23] H. Mete Soner, Motion of a set by the curvature of its boundary. Jour. Diff. Equations, Vol. 101 (2), 1993, pp. 313-372. | MR | Zbl

[24] M. Struwe, On the evolution of harmonic maps in higher dimensions. J. Diff. Geom., Vol. 28, 1988, pp. 485-502. | MR | Zbl

[25] M. Struwe. Variational Methods, Springer-Verlag, Berlin, 1990. | MR | Zbl

[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. | MR | Zbl

[27] Y. Kuramoto, Chemical Waves, Oscillations, and Turbulence, Springer-Verlag, Berlin, 1984. | Zbl