In this article, we investigate the boundary optimal control problem associated with Heat equation in a two-dimensional highly oscillating domain in which the control is applied periodically via Neumann condition on the oscillating part of the boundary. We characterize the optimal control in terms of unfolding operator and then study the homogenization to obtain two limit optimal control problems depending on the scalar parameters. In the limit optimal control problem, we obtain three controls, namely interior control, an interfacial control and a boundary control.
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