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Journal of Convex Analysis 11 (2004), No. 2, 363--385
Copyright Heldermann Verlag 2004

Homogenization of Evolution Problems in a Fiber Reinforced Structure

Michel Bellieud
Dep. de Mathematiques, Universite de Perpignan, 52 av. de Villeneuve, 66100 Perpignan, France,


We study the homogenization of parabolic or hyperbolic equations like $$ \rho_\epsilon(x){\partial^n u_\epsilon \over \partial t^n}- div(a_\epsilon(x) \nabla u_\epsilon) =f $$ on $\Omega\times (0, T)$ plus {\sl boundary conditions}, $n \in \{1,2\}$, where the coefficients $a_\epsilon$ and $\rho_\epsilon$ takes values of very different order on an $\epsilon$-periodic subset $T_\epsilon \subset \Omega$ (fibered structure) and elsewhere. We find a non local effective equation deduced from a homogenized system of several equations.

Keywords: homogenization, fiber structures, two-scale convergence, Γ-convergence.

MSC 2000: 35B40, 35J55, 74B05, 74K10, 74Q15.

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