Homogenization of Evolution Problems in a Fiber Reinforced Structure

M. Bellieud

Journal of convex analysis, Tome 11 (2004) no. 2, pp. 363-385

Résumé

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.

Détail

Mots-clés : homogenization, fiber structures, two-scale convergence, Γ-convergence