A Generalized Review on Homogenization and Two-Scale Convergence

Abstract

We study homogenization and two-scale convergence. Homogenization is a mathematical concept that makes it possible to develop a global model of the behaviour of a physical structure evolving in a heterogeneous structure. The behaviour of this physical structure will therefore be studied in a homogeneous environment, which greatly facilitates calculations. The two-scale convergence method was introduced by Nguetseng and later developed by Allaire. It is a particular form of weak convergence, a convergence between weak convergence GÉRARD ZONGO et al. 54 and strong convergence. The two-scale convergence simplifies the proof of homogenization theory. The method evolved very quickly and has been extended to several cases depending on the functional space.