Ginzburg-Landau方程的吸引子及其Hausdorff维数估计

The attractor of the complex Ginzburg-Landau equation and the estimate of its dimensionality of Hausdorff

作者在三维空间中研究带2σ次非线性项的复值G inzburg-L andau方程,通过先验估计的方法,在适当的σ的假设下,获得该方程周期边值问题整体吸引子的存在性,且对整体吸引子进行H ausdorff维数估计。

We study the complex Ginzburg-Landau equation that has the 2σ-th power of the nonlinear term. When the a is estimated appropriately,by using the method of priori estimate,we get the existence of the global attractor of this equation with the problem of period and border value and we study the dimensionality of Hausdorff of the global attractor.