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Optimal distributed control of the Cahn-Hilliard-Brinkman system with regular potential. (English) Zbl 1429.49009
In this paper, the authors establish some results concerning the well posedness of solutions for three dimensional Cahn-Hilliard-Brinkman system and prove some stability estimates which are necessary for the analysis of the control problem. They prove the main results of this paper, namely, the existence of a solution to the optimal control problem, the Frèchet differentiability of the control-to-state operator as well as the first-order necessary optimality conditions for problem.
MSC:
49J20 Existence theories for optimal control problems involving partial differential equations
49J50 Fréchet and Gateaux differentiability in optimization
49K20 Optimality conditions for problems involving partial differential equations
92C50 Medical applications (general)
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