Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 16, pp. 1-12.
Title: Darcy-type law associated to an optimal control problem
Authors: T. Muthukumar (Indian Inst. of Science, Bangalore, India)
A. K. Nandakumaran (Indian Inst. of Science, Bangalore, India)
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.
Submitted August 24, 2007. Published February 01, 2008.
Math Subject Classifications: 35B27, 49J20, 76D07.
Key Words: Homogenization; two-scale convergence; stokes
equation; optimal control; porous medium.