Optimal control problem governed by wave equation in an oscillating domain and homogenization

In this article, we consider the optimal control problem governed by the wave equation in a 2-dimensional domain \(\Omega _{\epsilon }\) ${\mathrm{\Omega }}_{ϵ}$ in which the state equation and the cost functional involves highly oscillating periodic coefficients \(A^\epsilon \) $A^{ϵ}$ and \(B^\epsilon \) $B^{ϵ}$ , respectively. This paper aims to examine the limiting behavior of optimal control and state and identify the limit optimal control problem, which involves the influences of the oscillating coefficients.