Boundary Temperature Control for Thermally Coupled Navier-Stokes Equations
In this paper the optimal control problem for the thermally coupled incompressible Navier-Stokes equations by the Dirichelet boundary temperature control is discussed. Well-posedness and existence of the optimal control for the finite-time horizon problem and optimal control problem for the stationary equations are established. Necessary optimality conditions are also obtained.
1991 Mathematics Subject Classification76D05 93C20 49B22
Key words and phrasesBoussinesq equation boundary temperature control necessary optimality condition
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- [DI]M.C.Desai and K.Ito, Optimal Control of Navier-Stokes Equations, SIAM J. Control & Optim., to appear (1994).Google Scholar
- [GR]V.Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations ,Springer-Verlag, Berlin, 1984.Google Scholar
- [IST1]K.Ito, J.S.Scroggs and H.T.Tran, Mathematical issues in optimal design of a vapor transport reactor, Proceeding of IMA workshop on Flow Control, ed by M.Gunzburger, (1993).Google Scholar
- [IST2]K.Ito, J.S.Scroggs and H.T.Tran, Optimal Control of Thermally Coupled Navier Stokes Equations, submitted to SIAM J. Control & Optim, (1993).Google Scholar
- [Tel]R.Temam, Navier-Stokes Equations and Nonlinear Functional Analysis ,SIAM, Philadelphia, 1983.Google Scholar
- [WvW]Wolf von Wahl, The Equations of Navier-Stokes and Abstract Parabolic Equations ,Vieweg, Braunschweig 1985.Google Scholar
- [Yo]K.Yosida, Functional Analysis ,Springer-Verlag, New York.Google Scholar