Ricerche di Matematica

, Volume 61, Issue 2, pp 231–244

The effective conductivity equation for a highly heterogeneous periodic medium

Authors

  • Hamid Charef
    • Département de mathématiquesUniversité du Sud Toulon-Var
    • Département de mathématiquesUniversité du Sud Toulon-Var
Article

DOI: 10.1007/s11587-011-0126-9

Cite this article as:
Charef, H. & Sili, A. Ricerche mat. (2012) 61: 231. doi:10.1007/s11587-011-0126-9

Abstract

We consider the homogenization of a conductivity equation for a medium made up of a set \({F_\varepsilon}\) (\({\varepsilon}\) being the size of the period of the medium) of highly conductive vertical fibers surrounded by another material (the matrix) assumed to be a poor conductor. The conductivity coefficients in the fibers behave as \({\frac{1}{\varepsilon^2}}\) while whose of the matrix behave as \({\varepsilon^2}\) . We show that the homogenized problem consists of an equality of the kind u(x) = m(x) f (x) where u denotes the macroscopic temperature, f the source term and m(x) a coefficient given by solving some cell equation.

Keywords

HomogenizationAnisotropyConductivityFibers

Mathematics Subject Classification (2010)

35B2774QXX76M50
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© Università degli Studi di Napoli "Federico II" 2011