@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] Level set approach to mean curvature flow in arbitrary codimension. J. Diff. Geom., Vol. 43, 1996, pp. 693-737. | MR | Zbl
and ,[2] Front propagation and phase field theory. SIAM J. Cont. Opt., Vol. 31 (2), 1993, pp. 439-469. | MR | Zbl
, , and ,[3] Vortex annihilation in nonlinear heat flow for Ginzburg-Landau systems. European J. Appl. Math., Vol. 6(2), 1995, pp. 115-126. | MR | Zbl
, , , and ,[4] and F HÉLEIN, Asymptotics for the minimization of a Ginzburg-Landau functional. Calc. Var., Vol. 1, 1993, pp. 123-148. | MR | Zbl
, ,[5] Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994. | MR | Zbl
, , ,[6] Quantization effects for -Δu = u(1 - |u|2) in R2. Archive Rat. Mech. Anal., Vol. 126, 1994, pp. 35-58. | MR | Zbl
, , and ,[7] Generation and propagation of the interface for reaction-diffusion equations. Jour. Diff. Equations, Vol. 96, 1992, pp. 116-141. | MR | Zbl
,[8] Existence and partial regularity results for the heat flow for harmonic maps. Math Z., Vol. 201, 1989, pp. 83-103. | EuDML | MR | Zbl
and ,[9] of vortices in Ginzburg-Landau theories with applications to superconductivity. Physica D, Vol. 77, 1994, pp. 383-404. | MR | Zbl
[10] Phase transitions and generalized motion by curvature. Comm. Pure Appl. Math., Vol. 65, 1992, pp. 1097-1123. | MR | Zbl
, , and ,[11] 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] Fully nonlinear phase field equations and generalized mean curvature motion. Comm PDE, Vol. 20, 1995, pp. 233-265. | MR | Zbl
,[13] Lower bounds for generalized Ginzburg-Landau functionals, center for Nonlinear Analysis Research Report No. 95-NA-020, 1995.
,[14] Dynamics of Ginzburg-Landau vortices, Arch. Rat. Mech. Anal., Vol. 142, 1998, pp. 99-125. | MR | Zbl
and ,[15] A certain property of solutions of parabolic equations with measurable coefficients. Math. USSR Izvestia, Vol. 16 (1), 1981, pp. 151-164. | Zbl
and ,[16] Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, RI, 1968.
, , and .[17] 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] Some dynamical properties of Ginzburg-Landau vortices. Comm. Pure Appl. Math., Vol. 49 (4), 1996, pp. 323-359. | MR | Zbl
,[19] Vortices in complex scalar fields. Physica D, Vol. 43, 1990, pp. 385-406. | MR | Zbl
,[20] Motion of vortex lines in the Ginzburg-Landau model. Physica D, Vol. 47, 1991, pp. 353-360. | MR | Zbl
and ,[21] Self-induced motion of line vortices. Quart. Appl. Math., Vol. 49 (1), 1991, pp. 1-9. | MR | Zbl
,[22] Analytic aspects of the harmonic map problem, In S.S. Chern, editor, Seminar on Nonlinear Partial Differential Equations. Springer, Berlin, 1984. | MR | Zbl
,[23] Motion of a set by the curvature of its boundary. Jour. Diff. Equations, Vol. 101 (2), 1993, pp. 313-372. | MR | Zbl
,[24] On the evolution of harmonic maps in higher dimensions. J. Diff. Geom., Vol. 28, 1988, pp. 485-502. | MR | Zbl
,[25] Variational Methods, Springer-Verlag, Berlin, 1990. | MR | Zbl
.[26] 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] Chemical Waves, Oscillations, and Turbulence, Springer-Verlag, Berlin, 1984. | Zbl
,