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Table des matières de ce fascicule | Article précédent | Article suivant Jerrard, Robert L.; Soner, Halil Mete
Scaling limits and regularity results for a class of Ginzburg-Landau systems. Annales de l'institut Henri Poincaré (C) Analyse non linéaire, 16 no. 4 (1999), p. 423-466
Texte intégral djvu | pdf | Analyses MR 1697561 | Zbl 0944.35006 | 6 citations dans Numdam
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[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 1412682 | Zbl 0868.35046 [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 1205984 | Zbl 0785.35049 [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 1331494 | Zbl 0845.35042 [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 1261720 | Zbl 0834.35014 [5] F. Bethuel, H. Brezis, F. Hélein, Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994. MR 1269538 | Zbl 0802.35142 [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 1268048 | Zbl 0809.35019 [7] X. Chen, Generation and propagation of the interface for reaction-diffusion equations. Jour. Diff. Equations, Vol. 96, 1992, pp. 116-141. MR 1153311 | Zbl 0765.35024 [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.
Article | MR 990191 | Zbl 0652.58024 [9] W.E., Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Physica D, Vol. 77, 1994, pp. 383-404. MR 1297726 | Zbl 0814.34039 [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 1177477 | Zbl 0801.35045 [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 1237490 | Zbl 0784.53035 [12] R.L. Jerrard, Fully nonlinear phase field equations and generalized mean curvature motion. Comm PDE, Vol. 20, 1995, pp. 233-265. MR 1312705 | Zbl 0860.35063 [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 1629646 | Zbl 0923.35167 [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 0464.35035 [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 1353261 | Zbl 0845.35052 [18] F.H. Lin, Some dynamical properties of Ginzburg-Landau vortices. Comm. Pure Appl. Math., Vol. 49 (4), 1996, pp. 323-359. MR 1376654 | Zbl 0853.35058 [19] J.C. Neu, Vortices in complex scalar fields. Physica D, Vol. 43, 1990, pp. 385-406. MR 1067918 | Zbl 0711.35024 [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 1098255 | Zbl 0728.35090 [21] J. Rubinstein, Self-induced motion of line vortices. Quart. Appl. Math., Vol. 49 (1), 1991, pp. 1-9. MR 1096227 | Zbl 0728.35118 [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 765241 | Zbl 0551.58011 [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 1204331 | Zbl 0769.35070 [24] M. Struwe, On the evolution of harmonic maps in higher dimensions. J. Diff. Geom., Vol. 28, 1988, pp. 485-502. MR 965226 | Zbl 0631.58004 [25] M. Struwe. Variational Methods, Springer-Verlag, Berlin, 1990. MR 1078018 | Zbl 0746.49010 [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 1269674 | Zbl 0809.35031 [27] Y. Kuramoto, Chemical Waves, Oscillations, and Turbulence, Springer-Verlag, Berlin, 1984. Zbl 0558.76051
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