具有局部周期高振荡边界薄区域的开折算子方法
Unfolding operator method for thin domains with a locally periodic highly oscillatory boundary
摘要：
本文研究了具有齐次Neumann边界条件的二维薄区域中的泊松方程解的行为，该区域在边界处具有局部周期振荡.振荡使得振荡的振幅和周期两者可以在空间中变化。通过将展开算子方法推广到局部周期介质的情形，得到了均匀化极限问题和一个修正结果。我们强调的事实是，本文中开发的技术可以适应其他局部周期性的情况下，如网状或穿孔域的周期可能是空间依赖性的。
英文摘要：
We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media. We emphasize the fact that the techniques developed in this paper can be adapted to other locally periodic cases like reticulated or perforated domains where the period may be space-dependent.
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