Preprint

Analysis of optimal boundary control of the Boussinesq approximation

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

65M06 Finite difference methods

76D05 Navier-Stokes equations

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