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In this paper we study optimal control problem for non localCahn-Hilliard-Brinkman system which models phase separation of binary fluids inporous media. We consider the system in two dimensional bounded domain withregular potential. We extend recently proved existence of weak solution resultsfor such a system and prove the existence of strong solution under certainassumptions on the forcing term and initial datum. Further using our regularityresults, we study the tracking type optimal control problem. We prove theexistence of an optimal control and establish the first order optimalitycondition. Lastly, we characterize optimal control in terms of the solution ofcorresponding adjoint system. The existence of solution for the adjoint systemis also established.

Nonlocal Cahn-Hilliard-Brinkman System with regular potential: Regularity and optimal control