On Some Homogenization Problems

This expository paper presents some recent results on the “homogenization” process which consists in “approximating” a nonhomogeneous material with a periodic structure by a homogeneous material. Examples of non homogeneous materials are given by composite materials or by performed materials. The approximation is valid when the size ϵ of the period tends to 0. Actually one obtains in some cases higher order terms in the expansion of the state of the system in terms of “powers” of ϵ, with an ansatz of the type of “multiple scale” variables.