Homogenization of distributive optimal control problem governed by Stokes system in an oscillating domain

Abstract

The present article deals with the homogenization of a distributive optimal control problem (OCP) subjected to the more generalized stationary Stokes equation involving unidirectional oscillating coefficients posed in a two-dimensional oscillating domain. The cost functional considered is of the Dirichlet type involving a unidirectional oscillating coefficient matrix. We characterize the optimal control and study the homogenization of this OCP with the aid of the unfolding operator. Due to the presence of oscillating matrices both in the governing Stokes equations and the cost functional, one obtains the limit OCP involving a perturbed tensor in the convergence analysis.