Electron. J. Diff. Eqns., Vol. 2000(2000), No. 42, pp. 125.
Spectrum of the linearized operator for the GinzburgLandau equation
TaiChia Lin
Abstract:
We study the spectrum of the linearized operator for the
GinzburgLandau 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.
Submitted May 1, 2000. Published June 9, 2000.
Math Subject Classifications: 35P15, 35K55, 35Q55.
Key Words: GinzburgLandau equation, spectrum, vortex dynamics, superfluid.
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TaiChia Lin
Department of Mathematics
National ChungCheng University
ChiaYi, Taiwan, ROC
email: tclin@math.ccu.edu.tw 
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