ABSTRACT
We consider a Dirichlet boundary control problem posed in an oscillating boundary domain governed by a biharmonic equation. Homogenization of a PDE with a non-homogeneous Dirichlet boundary condition on the oscillating boundary is one of the hardest problems. Here, we study the homogenization of the problem by converting it into an equivalent interior control problem. The convergence of the optimal solution is studied using periodic unfolding operator.
Acknowledgments
We acknowledge the referees for their careful and meticulous reading of the manuscript, and their comments immensely helped us in improving the presentation of the manuscript. The authors wish to thank Prof. A. K. Nandakumaran for stimulating discussions on the topic.
Disclosure statement
No potential conflict of interest was reported by the authors.