Homogenization of optimal control problems in perforated domains via periodic unfolding method

This article aims to study the limiting behaviors of optimal control problems based on an elliptic boundary value problem with highly oscillating coefficients in a periodically perforated domain. We consider two different types of cost functionals, the -cost functional and the Dirichlet cost functio...

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Bibliographic Details
Published in:Applicable analysis 2016-11, Vol.95 (11), p.2517-2534
Main Author: Cabarrubias, Bituin
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary value problems
Constraining
Control theory
Dirichlet problem
elliptic problems
Functionals
Homogenization
Homogenizing
Mathematical analysis
Optimal control
Oscillating
perforated domains
unfolding method
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Summary:This article aims to study the limiting behaviors of optimal control problems based on an elliptic boundary value problem with highly oscillating coefficients in a periodically perforated domain. We consider two different types of cost functionals, the -cost functional and the Dirichlet cost functional. We use the periodic unfolding method for perforated domains to homogenize the problems. Moreover, we prove that under this method, only the energy corresponding to the former cost functional converges.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2015.1094799