A new sharp estimate on the dimension of the attractor for the Dirichlet problem of the complex Ginzburg-Landau equation

摘要

Using the improved lower bound on the sum of the eigenvalues of the DirichletLaplacian proved by A. D. Melas (Proc. Amer. Math. Soc. \textbf{131} (2003)631-636), we report a new and sharp estimate for the dimension of the globalattractor associated to the complex Ginzburg-Landau equation supplemented withDirichlet boundary conditions.