Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 06, pp. 1-27.

Title: Homogenization and correctors for composite media with 
       coated and highly anisotropic fibers

Author: Ahmed Boughammoura (Institut Superieur d'Informatique, Tunisia)

Abstract:
 This article presents the homogenization of a quasilinear
 elliptic-parabolic problem in  an $\varepsilon$-periodic medium
 consisting of  a set of highly anisotropic fibers surrounded by
 coating layers, the whole  being embedded in a third material
 having an order 1 conductivity. The conductivity along the
 fibers  is of order 1 but the conductivities in the transverse
 directions and in the  coatings are scaled by $\mu=o(\varepsilon)$
 and $\varepsilon^p$, as $\varepsilon\to 0$,  respectively.  The heat
 flux are quasilinear, monotone functions of the temperature
 gradient. The heat capacities of the medium components are bounded
 but may vanish on certain subdomains, so the problem may become
 degenerate. By using the two-scale convergence method, we can
 derive the two-scale homogenized systems and prove some
 corrector-type results depending on the critical  value
 $\gamma=\lim_{\varepsilon\searrow 0}\varepsilon^p/\mu$.

Submitted August 17, 2011. Published January 10, 2012.
Math Subject Classifications: 35B27, 35B40, 35K65, 76M50.
Key Words: Homogenization; correctors; monotone problem; 
           composite media; coatings; highly anisotropic fibers.