Homogenization

Summary

Homogenization is the study of partial differential equations whose coefficients oscillate on a small scale $\varepsilon$, in the limit $\varepsilon \to 0$. The solutions converge to the solution of a homogenized equation with effective, slowly varying or constant coefficients. For periodic media the effective coefficients are computed from a cell problem on one period. It explains, for example, the effective conductivity of a composite material made of a fine mixture of two materials.