Author(s) :
Günter Bärwolff
,
Michael Hinze
Preprint series of the Institute of Mathematics, Technische Universität Berlin
MSC 2000
- 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
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65M06 Finite difference methods
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76D05 Navier-Stokes equations
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76D55 Flow control and optimization
Abstract :
In the present paper we complement the work in preprint 15-03 of the Inst. of Mathematics of the TU Berlin (also published in ZAMM 86(2006)6) with presenting the analytical framework for general optimal boundary control problems of the Boussinesq approximation. We prove existence of optimal controls, use results of H. Gajewski to prove existence and uniqueness of solutions to state and the adjoint system, and derive first order necessary as well as second order sufficient optimality conditions.
Keywords :
Time--dependent Boussinesq approximation, optimal boundary control, optimality conditions