Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 80, pp. 1-20.

Title: Optimal control problem for Stokes systems: asymptotic analysis via unfolding
method in a perforated domain
       
Authors: Swati Garg (Indian Inst. of Technology Ropar, Punjab, India)
         Bidhan Chandra Sardar (Indian Inst. of Technology Ropar, Punjab, India)

Abstract:
This article's subject matter is the study of the asymptotic analysis of the
optimal control problem  (OCP) constrained by the stationary Stokes equations
in a periodically perforated domain.
We subject the interior region of it with distributive controls.
The Stokes operator considered involves the oscillating coefficients for the
state equations. We characterize the optimal control and, upon employing the
method of periodic unfolding, establish the convergence of the solutions of the
considered OCP to the solutions of the limit OCP governed by stationary Stokes
equations over a non-perforated domain. The convergence of the cost functional
is also established.

Submitted May 23, 2023. Published December 06, 2023.
Math Subject Classifications: 35B27, 35B40, 35Q93, 49J20, 76D07.
Key Words: Stokes equations; homogenization; optimal control; perforated domain; unfolding operator.