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Piecewise optimal distributed controls for 2D Boussinesq equations. (English) Zbl 0951.35108
The authors consider the velocity and temperature tracking problem for viscous incompressible thermally convected flows in two dimensions (which is similar to the velocity tracking problem for viscous incompressible flows). This problem is formulated as a piecewise (in time) distributed optimal control problem for the Boussinesq equations. The semidiscrete (in time) approximation of the piecewise optimal control problem is also studied. The main theorem asserts that the \(L^2\) and \(H^1\) norms of the difference between the controlled state and the desired state both decay to zero exponentially in time. A similar result is obtained for the semidiscrete approximation of the piecewise optimal control problem.
Reviewer: C.Popa (Iaşi)

MSC:
35Q30 Navier-Stokes equations
35B37 PDE in connection with control problems (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
49M25 Discrete approximations in optimal control
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