In this paper, we study an optimal control problem for nonlocal Cahn-Hilliard-Brinkman system, which models phase separation of binary fluids in porous media. The system evolves with regular potential in a two-dimensional bounded domain. We extend the existence of weak solution results for the system to prove the existence of strong solution under extra assumptions on the forcing term and initial datum. Further, using our regularity results, we study the tracking type optimal control problem. We prove the existence of optimal control and establish the first-order optimality condition. Lastly, we characterise optimal control in terms of the solution of the corresponding adjoint system. The existence of the solution for the adjoint system is also established.

在本文中，我们研究了非局部Cahn-Hilliard-Brinkman系统的最优控制问题，该系统对多孔介质中二元流体的相分离进行建模。该系统在二维有界域中具有规则的势能。我们为系统扩展了弱解结果的存在性，以证明在强迫项和初始基准的额外假设下强解的存在性。此外，使用我们的规律性结果，我们研究了跟踪类型的最优控制问题。我们证明了最优控制的存在并建立了一阶最优条件。最后，我们根据相应的伴随系统的解来表征最优控制。还确定了伴随系统解决方案的存在。