纤维均质化
Fibre Homogenisation
摘要：
在这篇文章中，我们提出了一种新的方法来研究渐近行为，与阶尖误差估计，参数依赖的算子族的预解式。该方法适用于研究的微分方程的快速振荡系数的背景下，二阶偏微分方程系统和麦克斯韦系统。这产生了非标准的均质化结果，其特征在于相关Floquet-Bloch PDE的“纤维式”均质化。这些纤维均质化的预解式被证明是渐近等价于整个类的运营商的家庭，包括通过标准均质化方法获得的。
英文摘要：
In this article we present a novel method for studying the asymptotic behaviour, with order-sharp error estimates, of the resolvents of parameter-dependent operator families. The method is applied to the study of differential equations with rapidly oscillating coefficients in the context of second-order PDE systems and the Maxwell system. This produces a non-standard homogenisation result that is characterised by `fibre-wise' homogenisation of the related Floquet-Bloch PDEs. These fibre-homogenised resolvents are shown to be asymptotically equivalent to a whole class of operator families, including those obtained by standard homogenisation methods.
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