Electron. J. Diff. Eqns., Vol. 2000(2000), No. 42, pp. 1-25.

Spectrum of the linearized operator for the Ginzburg-Landau equation

Tai-Chia Lin

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.

Show me the PDF file (234K), TEX file, and other files for this article.

Tai-Chia Lin
Department of Mathematics
National Chung-Cheng University
Chia-Yi, Taiwan, ROC
e-mail: tclin@math.ccu.edu.tw

Return to the EJDE web page