Homogenization of variational equations and inequalities with small oscillating parameters. Application to the study of thin film unstationary lubrication flow

Double scale homogenization is used to average stationary equation or inequ alities in which both highly oscillating variables and parameters appear. W e demonstrate how the limit is obtained using a two-stage procedure, firstl y by carrying out a classical homogenization process by freezing the oscill ating parameter, then by averaging the result with respect to this paramete r. These results allow us to average the pressure for a newtonian fluid in a narrow gap between two rough unstationnary surfaces. (C) 2000 Academie de s sciences/Editions scientifiques et medicales Elsevier SAS.