论文标题
Bi-Lipschitz Mane投影仪和复杂的Ginzburg-Landau方程的有限维度减少
Bi-Lipschitz Mane projectors and finite-dimensional reduction for complex Ginzburg-Landau equation
论文作者
论文摘要
我们提出了一种新的方法，用于建立具有交叉扩散项的半连接抛物线系统的极限动力学（用Bi-lipschitz mane投影仪），并在具有周期性边界条件的3D复杂Ginzburg-Landau方程的模型示例上进行了说明。该方法结合了卖出和槌锤发明的所谓空间平均原理，以及来自交叉扩散项的快速振荡的时间平均。
We present a new method of establishing the finite-dimensionality of limit dynamics (in terms of bi-Lipschitz Mane projectors) for semilinear parabolic systems with cross diffusion terms and illustrate it on the model example of 3D complex Ginzburg-Landau equation with periodic boundary conditions. The method combines the so-called spatial-averaging principle invented by Sell and Mallet-Paret with temporal averaging of rapid oscillations which come from cross-diffusion terms.
