Rivière, Tristan:
Asymptotic analysis for the Ginzburg-Landau equations
Bollettino dell'Unione Matematica Italiana Serie 8 2-B (1999), fasc. n.3, p. 537-575, Unione Matematica Italiana (English)
pdf (363 Kb), djvu (446 Kb). | MR1719570 | Zbl 0939.35199
Sunto
Questo lavoro costituisce un survey sui problemi di limite asintotico per le soluzioni delle equazioni di Ginzburg-Landau in dimensione due. Vengono presentati essenzialmente i risultati di [BBH] e [BR] sulla formazione ed il comportamento asintotico dei vortici in un dominio bidimensionale nel caso fortemente repulsivo (large $K$ limit).
Referenze Bibliografiche
[1]
L.
ALMEIDA
-
F.
BETHUEL
,
Multiplicity results for the Ginzburg-Landau equation in presence of symmetries,
Houston J. Math.,
23 (
1997), 733-764. |
MR 1687389 |
Zbl 0901.35029[2]
L.
ALMEIDA
-
F.
BETHUEL
,
Topological Methods for the Ginzburg-Landau Equations,
J. Math. Pures Appl.,
77 (
1998), 1-49. |
MR 1617594 |
Zbl 0904.35023[3]
F.
BETHUEL
-
H.
BREZIS
-
F.
HÉLEIN
,
Asymptotics for the minimization of a Ginzburg-Landau functional,
Calculus of variations and PDE
1 (
1993), 123-148. |
MR 1261720 |
Zbl 0834.35014[5]
F.
BETHUEL
-
T.
RIVIÈRE
,
Vortices for a variational problem related to supraconductivity,
Ann. Inst. Henri Poincaré (analyse non linéaire),
12, 3 (
1995), 243-303. |
fulltext mini-dml |
MR 1340265 |
Zbl 0842.35119[8]
R.
JERRARD
-
M.
SONER
,
Dynamics of Ginzburg-Landau Vortices, to appear in
Arch. Rat. Mech. Anal.
|
Zbl 0923.35167[9]
F. H.
LIN
,
Some Dynamical properties of Ginzburg-Landau Vortices,
Comm. Pure and App. Math (
1996), 323-359.
A remark on the previous paper...,
Comm. Pure and App. Math. (
1996), 361-364. |
MR 1376654 |
Zbl 0853.35059[10]
F. H.
LIN
,
Complex Ginzburg-Landau Equations and Dynamics of Vortices, Filaments and Codimension 2 Submanifolds, preprint (
1997). |
MR 1491752 |
Zbl 0932.35121[11]
F. H.
LIN
-
T. C.
LIN
,
Minimax solutions of the Ginzburg-Landau equations, preprint (
1996). |
Zbl 0876.49006[12]
F. H.
LIN
-
T.
RIVIÈRE
,
Complex Ginzburg-Landau Equations in High Dimensions and Codimension two Area Minimizing Currents, to appear. |
Zbl 0939.35056[13]
F.
PACARD
-
T.
RIVIÈRE
, Construction of Ginzburg-Landau solutions having regular zero-set for large coupling constant, preprint CMLA ENS-Cachan (1998).
[14]
F.
PACARD
-
T.
RIVIÈRE
, A uniqueness result for the minimizers of the Ginzburg-Landau Functional, preprint CMLA ENS-Cachan (1998).
[16]
D.
SAINT-JAMES
-
G.
SARMA
-
E. J.
THOMAS
, Type II Superconductivity, Pergamon Press (1969).
[17]
S.
SERFATY
,
Local minimizers for the Ginzburg-Landau energy near Critical Magnetic Field, preprint Orsay (
1997). |
Zbl 0944.49007[18]
M.
STRUWE
,
On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2-dimensions,
J. Diff. Int. Equations,
7 (
1994), 1613-1624 and
Erratum in
J. Diff. Int.
|
MR 1269674 |
Zbl 0809.35031