In this work, we study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of the periodic heterogeneity. The homogenized tensor is obtained in terms of the first Bloch eigenvalue. The higher Bloch modes do not contribute to the homogenization limit. The main difficulty is the presence of two parameters which requires us to obtain uniform bounds on the Bloch spectral data in various regimes of the parameter.

中文翻译：

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同质化和奇异扰动的组合效应：布洛赫波方法

在这项工作中，我们研究了具有四阶奇异扰动的周期性非均质介质的布洛赫波均匀化。我们根据奇异扰动的相对强度和周期性异质性的长度尺度恢复不同的均质化机制。均质化张量是根据第一个布洛赫特征值获得的。较高的 Bloch 模式对均质化限制没有贡献。主要困难是存在两个参数，这要求我们在参数的各种状态下获得 Bloch 光谱数据的统一界限。