In this article, we consider the optimal control problem governed by the wave equation in a 2-dimensional domain \(\Omega _{\epsilon }\) in which the state equation and the cost functional involves highly oscillating periodic coefficients \(A^\epsilon \) and \(B^\epsilon \), 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.

中文翻译：

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振荡域波动方程和均匀化的最优控制问题

在本文中，我们考虑二维域\(\Omega _{\epsilon }\)中波动方程控制的最优控制问题，其中状态方程和成本函数涉及高度振荡的周期系数\(A^分别为\epsilon \)和\(B^\epsilon \)。本文旨在研究最优控制和状态的极限行为，并识别涉及振荡系数影响的极限最优控制问题。