A GENERALIZED REVIEW ON HOMOGENIZATION AND TWO-SCALE CONVERGENCE
- Journal of Mathematical Sciences: Advances and Applications , 58 : 53-105
Résumé
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 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.
Mots-clés
two-scale convergence, multiscale convergence, weak convergence, strong convergence, homogenization.