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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Introduction
verfasst von : Zhongwei Shen
Erschienen in: Periodic Homogenization of Elliptic Systems
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Partial differential equations and systems with rapidly oscillating coefficients are used to model various physical phenomena in inhomogeneous or heterogeneous media, such as composite and perforated materials. Let ε > 0 be a small parameter, representing the inhomogeneity scale – the scale of the microstructure of an inhomogeneous medium. The local characteristics of the medium are described by functions of the form $$\mathit{A}(\mathit{x}/\varepsilon)$$ , which vary rapidly with respect to the space variables. Since ε is much smaller than the linear size of the domain where the physical process takes place, solving the corresponding boundary value problems for the partial differential equations directly by numerical methods may be costly.