Geodesic
Spectrum of the linearized operator for the Ginzburg-Landau equation
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the spectrum of the linearized operator for the Ginzburg-Landau equation about a symmetric vortex solution with degree one. We show that the smallest eigenvalue of the linearized operator has multiplicity two, and then we describe its behavior as a small parameter approaches zero. We also find a positive lower bound for all the other eigenvalues, and find estimates of the first eigenfunction. Then using these results, we give partial results on the dynamics of vortices in the nonlinear heat and Schrodinger equations.
Classification : 35P15, 35K55, 35Q55
Keywords: Ginzburg-Landau equation, spectrum, vortex dynamics, superfluid 
@article{EJDE_2000__2000__a148,
     author = {Lin, Tai-Chia},
     title = {Spectrum of the linearized operator for the {Ginzburg-Landau} equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a148/}
}
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Lin, Tai-Chia. Spectrum of the linearized operator for the Ginzburg-Landau equation. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a148/