Homogenization in algebras with mean value

Abstract

In several works, the theory of strongly continuous groups is used to build a framework for solving random homogenization problems. Following this idea, we present a detailed and comprehensive framework enabling one to solve homogenization problems in algebras with mean value, regardless of whether they are ergodic or not. We also state and prove a compactness result for Young measures in these algebras. As an important achievement we study the homogenization problem associated with a stochastic Ladyzhenskaya model for incompressible viscous flow, and we present and solve a few examples of homogenization problems related to nonergodic algebras.