Abstract

In the paper we consider a problem for complex Ginzburg–Landau equations in a medium with locally periodic small obstacles. It is assumed that the obstacle surface can have different conductivity coefficients. We prove that the trajectory attractors of this system converge in a certain weak topology to the trajectory attractors of the homogenized Ginzburg–Landau equations with an additional potential (in the critical case), without an additional potential (in the subcritical case) in the medium without obstacles, or disappear (in the supercritical case).

中文翻译：

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局部周期性微观结构域中金兹堡-朗道方程的吸引子：亚临界、临界和超临界情况

摘要

在本文中，我们考虑了具有局部周期性小障碍的介质中复杂的金兹堡-朗道方程的问题。假设障碍物表面可以具有不同的传导系数。我们证明该系统的轨迹吸引子以某种弱拓扑收敛到具有附加势（在临界情况下）的均质化Ginzburg-Landau方程的轨迹吸引子，而在介质中没有附加势（在亚临界情况下）没有障碍，或者消失（在超临界情况下）。