We study a concentration and homogenization problem modelling electrical conduction in a composite material. The novelty of the problem is due to the specific scaling of the physical quantities characterizing the dielectric component of the composite. This leads to the appearance of a peculiar displacement current governed by a Laplace–Beltrami pseudo-parabolic equation. This pseudo-parabolic character is present also in the homogenized equation, which is obtained by the unfolding technique.

中文翻译：

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涉及L aplace–B eltrami算子的异质介质中电的集中和均质化

我们研究了在复合材料中建模导电的浓度和均质化问题。该问题的新颖性是由于表征复合材料介电成分的物理量的特定比例。这导致出现由Laplace-Beltrami伪抛物线方程控制的特殊位移电流。该伪抛物线特征也存在于通过展开技术获得的均化方程中。