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

Article type: Research Article

Authors: Garg, Swati | Sardar, Bidhan Chandra^{; *}

Affiliations: Department of Mathematics, Indian Institute of Technology, Ropar, Punjab-140001, India

Correspondence: [*] Corresponding author. E-mails: bcsardar@iitrpr.ac.in, bcsardar31@gmail.com.

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.

Keywords: Homogenization, optimal control, oscillating boundary, unfolding operator, Stokes equations

DOI: 10.3233/ASY-231867

Journal: Asymptotic Analysis, vol. 136, no. 1, pp. 1-26, 2024