Electron. J. Differential Equations, Vol. 2023 (2023), No. 80, pp. 1-20.
Optimal control problem for Stokes systems: asymptotic analysis via unfolding
method in a perforated domain
Swati Garg, Bidhan Chandra Sardar
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 6, 2023.
Math Subject Classifications: 35B27, 35B40, 35Q93, 49J20, 76D07.
Key Words: Stokes equations; homogenization; optimal control; perforated domain; unfolding operator.
DOI: 10.58997/ejde.2023.80
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Swati Garg
Department of Mathematics
Indian Institute of Technology Ropar
Rupnagar-140001, Punjab, India
email: swati.19maz0006@iitrpr.ac.in, swatigargmks@gmail.com
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Bidhan Chandra Sardar
Department of Mathematics
Indian Institute of Technology Ropar
Rupnagar-140001, Punjab, India
email: bcsardar@iitrpr.ac.in
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