Darcy-type law associated to an optimal control problem

Abstract

The aim of this paper is to study the asymptotic behaviour (homogenization) of an optimal control problem in a periodically perforated domain with Dirichlet condition on the boundary of the holes. The optimal control problem considered here is governed by the Stokes system. The holes are assumed to be of the same order as that of the period. The homogenized limit of the Stokes system as well as its adjoint system arising from the optimal control problem is obtained. The convergence of the optimal control and cost functional is obtained on some specific control sets.

Keywords

• Homogenization
• two-scale convergence
• stokes
• equation
• optimal control
• porous medium