Scaling limits and regularity results for a class of Ginzburg-Landau systems
Robert L. Jerrard; Halil Mete Soner
Annales de l'I.H.P. Analyse non linéaire (1999)
- Volume: 16, Issue: 4, page 423-466
- ISSN: 0294-1449
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topJerrard, Robert L., and Soner, Halil Mete. "Scaling limits and regularity results for a class of Ginzburg-Landau systems." Annales de l'I.H.P. Analyse non linéaire 16.4 (1999): 423-466. <http://eudml.org/doc/78471>.
@article{Jerrard1999,
author = {Jerrard, Robert L., Soner, Halil Mete},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {-regularity theorems; mean curvature flow; partial regularity theorems uniform in },
language = {eng},
number = {4},
pages = {423-466},
publisher = {Gauthier-Villars},
title = {Scaling limits and regularity results for a class of Ginzburg-Landau systems},
url = {http://eudml.org/doc/78471},
volume = {16},
year = {1999},
}
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
PB - Gauthier-Villars
VL - 16
IS - 4
SP - 423
EP - 466
LA - eng
KW - -regularity theorems; mean curvature flow; partial regularity theorems uniform in
UR - http://eudml.org/doc/78471
ER -
References
top- [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. Zbl0868.35046MR1412682
- [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. Zbl0785.35049MR1205984
- [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. Zbl0845.35042MR1331494
- [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. Zbl0834.35014MR1261720
- [5] F. Bethuel, H. Brezis, F. Hélein,Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994. Zbl0802.35142MR1269538
- [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. Zbl0809.35019MR1268048
- [7] X. Chen, Generation and propagation of the interface for reaction-diffusion equations. Jour. Diff. Equations, Vol. 96, 1992, pp. 116-141. Zbl0765.35024MR1153311
- [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. Zbl0652.58024MR990191
- [9] W.E., Dynamicsof vortices in Ginzburg-Landau theories with applications to superconductivity. Physica D, Vol. 77, 1994, pp. 383-404. Zbl0814.34039MR1297726
- [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. Zbl0801.35045MR1177477
- [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. Zbl0784.53035MR1237490
- [12] R.L. Jerrard, Fully nonlinear phase field equations and generalized mean curvature motion. Comm PDE, Vol. 20, 1995, pp. 233-265. Zbl0860.35063MR1312705
- [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. Zbl0923.35167MR1629646
- [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. Zbl0464.35035
- [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. Zbl0845.35052MR1353261
- [18] F.H. Lin, Some dynamical properties of Ginzburg-Landau vortices. Comm. Pure Appl. Math., Vol. 49 (4), 1996, pp. 323-359. Zbl0853.35058MR1376654
- [19] J.C. Neu, Vortices in complex scalar fields. Physica D, Vol. 43, 1990, pp. 385-406. Zbl0711.35024MR1067918
- [20] L.M. Pismen and J. Rubinstein, Motion of vortex lines in the Ginzburg-Landau model. Physica D, Vol. 47, 1991, pp. 353-360. Zbl0728.35090MR1098255
- [21] J. Rubinstein, Self-induced motion of line vortices. Quart. Appl. Math., Vol. 49 (1), 1991, pp. 1-9. Zbl0728.35118MR1096227
- [22] R. Schoen, Analytic aspects of the harmonic map problem, In S.S. Chern, editor, Seminar on Nonlinear Partial Differential Equations. Springer, Berlin, 1984. Zbl0551.58011MR765241
- [23] H. Mete Soner, Motion of a set by the curvature of its boundary. Jour. Diff. Equations, Vol. 101 (2), 1993, pp. 313-372. Zbl0769.35070MR1204331
- [24] M. Struwe, On the evolution of harmonic maps in higher dimensions. J. Diff. Geom., Vol. 28, 1988, pp. 485-502. Zbl0631.58004MR965226
- [25] M. Struwe. Variational Methods, Springer-Verlag, Berlin, 1990. Zbl0746.49010MR1078018
- [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. Zbl0809.35031MR1269674
- [27] Y. Kuramoto, Chemical Waves, Oscillations, and Turbulence, Springer-Verlag, Berlin, 1984. Zbl0558.76051
Citations in EuDML Documents
top- Robert L. Jerrard, Vortex filament dynamics for Gross-Pitaevsky type equations
- F. Bethuel, G. Orlandi, D. Smets, Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics
- Luigi Ambrosio, Halil Mete Soner, A measure theoretic approach to higher codimension mean curvature flows
- F. Bethuel, G. Orlandi, Uniform estimates for the parabolic Ginzburg–Landau equation
- Fang Hua Lin, Chang You Wang, Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows
- Fabrice Bethuel, Giandomenico Orlandi, Didier Smets, Motion of concentration sets in Ginzburg-Landau equations
- F. Bethuel, G. Orlandi, Uniform estimates for the parabolic Ginzburg–Landau equation
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