Homogenization of evolution problems for a composite medium with very small and heavy inclusions

Bellieud, Michel

ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 266-284

Résumé

We study the homogenization of parabolic or hyperbolic equations like

$${\rho }_{\epsilon }\frac{{\partial }^n{u}_{\epsilon }}{\partial t^n}-\mathrm{div}\left(a_{\epsilon }\nabla u_{\epsilon }\right)=f\text{in}\Omega \times (0,T)+\text{boundary}\text{conditions},n\in \{1,2\},$$

when the coefficients ${\rho }_{\epsilon }$, $a_{\epsilon }$ (defined in $Ø$) take possibly high values on a $\epsilon$-periodic set of grain-like inclusions of vanishing measure. Memory effects arise in the limit problem.

Détail

DOI : 10.1051/cocv:2005007

Classification : 35K05, 35L05, 73B27
Keywords: homogenization, memory effects, grain-like inclusions