We present a new method of establishing the finite-dimensionality of limit dynamics (in terms of bi-Lipschitz Mané projectors) for semilinear parabolic systems with cross diffusion terms and illustrate it on the model example of three-dimensional 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.

中文翻译：

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Bi-Lipschitz Mané 投影仪和复杂 Ginzburg-Landau 方程的有限维约简

我们提出了一种新的方法来建立具有交叉扩散项的半线性抛物线系统的极限动力学的有限维数（根据双李普希茨马内投影仪），并在具有周期性的三维复杂 Ginzburg-Landau 方程的模型示例上进行说明。边界条件。该方法将 Sell 和 Mallet-Paret 发明的所谓空间平均原理与来自交叉扩散项的快速振荡的时间平均相结合。