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Preprint 10-2008

Analysis of optimal boundary control of the Boussinesq approximation

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Author(s) : Günter Bärwolff , Michael Hinze

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2008

MSC 2000

76D05 Navier-Stokes equations
76D55 Flow control and optimization

Abstract :
In the present paper we complement a recent applied work with presenting the analytical framework for general optimal boundary control problems of the Boussinesq approximation. We prove existence of optimal controls, use results of Gajewski (1975) 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

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