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Optimal controls of Boussinesq equations with state constraints. (English) Zbl 1100.49026
The paper considers an optimal control problem for a semilinear parabolic system (Boussinesq system) with controls in the right hand side of the equations, with Lipshitz continuous cost functional and with additional integral type state constraints. By means of a specialized penalty method necessary optimality conditions are obtained.

MSC:
49K20 Optimality conditions for problems involving partial differential equations
35Q30 Navier-Stokes equations
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