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

Abstract

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.

Keywords:

• Optimal control
• homogenization
• unfolding method
• perforated domains
• elliptic problems

AMS Subject Classifications:

• 35J56
• 35Q91
• 35Q93
• 49J21

Acknowledgements

The author would like to thank the Office of the Vice Chancellor for Research and Development of the University of the Philippines for the financial support, the two reviewers for constructive criticism and to Dr. Ravi Prakash for the suggestions for the improvement of this work.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Office of the Vice Chancellor for Research and Development of the University of the Philippines [OVCRD Project Number 131310 PhDIA].