Department of Mathematics
National Chung-Cheng University
Chia-Yi, Taiwan, ROC
e-mail: tclin@math.ccu.edu.tw
Tai-Chia Lin
Abstract:
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.
Submitted May 1, 2000. Published June 9, 2000.
Math Subject Classifications: 35P15, 35K55, 35Q55.
Key Words: Ginzburg-Landau equation, spectrum, vortex dynamics, superfluid.
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Tai-Chia Lin Department of Mathematics National Chung-Cheng University Chia-Yi, Taiwan, ROC e-mail: tclin@math.ccu.edu.tw |
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