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Boundary Temperature Control for Thermally Coupled Navier-Stokes Equations

  • Kazufumi Ito
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 118)

Abstract

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 Classification

76D05 93C20 49B22 

Key words and phrases

Boussinesq equation boundary temperature control necessary optimality condition 

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References

  1. [AT]
    F.Abergel and R.Temam, On some control problems in fluid mechanics, Theoretical and Computational Fluid Mechanics, 1 (1990), 303–325.zbMATHCrossRefGoogle Scholar
  2. [CF]
    P. Constantin and C. Foias, Navier-Stokes Equations ,The University of Chicago Press, Chicago, 1988.zbMATHGoogle Scholar
  3. [DI]
    M.C.Desai and K.Ito, Optimal Control of Navier-Stokes Equations, SIAM J. Control & Optim., to appear (1994).Google Scholar
  4. [ET]
    I.Ekeland and R.Temam, Convex Analysis and Variational Problems ,North Holland, Amsterdam (1976).zbMATHGoogle Scholar
  5. [Gl]
    R.Glowinski, Numerical Methods for Nonlinear Variational Problems ,Springer-Verlag, Berlin, 1984.zbMATHGoogle Scholar
  6. [GR]
    V.Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations ,Springer-Verlag, Berlin, 1984.Google Scholar
  7. [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
  8. [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
  9. [LM]
    J.L.Lions and E.Magenes,Non-homogeneous Boundary Value Problems and Applications ,Vol I,II, Springer-Verlag, New York, 1972.CrossRefGoogle Scholar
  10. [MZ]
    H.Maurer and J.Zowe, First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems, Math Programming, 16 (1979), 98–110.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [Ta]
    H.Tanabe, Equations of Evolution ,Pitman, San Francisco, 1979.zbMATHGoogle Scholar
  12. [Tel]
    R.Temam, Navier-Stokes Equations and Nonlinear Functional Analysis ,SIAM, Philadelphia, 1983.Google Scholar
  13. [Te2]
    R.Temam, Infinite Dimensional Dynamical Systems in Mechanics and Pysics ,Appl. Math. Sci. 68, Springer-Verlag, New York, 1988.CrossRefGoogle Scholar
  14. [Tr]
    G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems ,Plenum Press, New York, 1987.zbMATHGoogle Scholar
  15. [WvW]
    Wolf von Wahl, The Equations of Navier-Stokes and Abstract Parabolic Equations ,Vieweg, Braunschweig 1985.Google Scholar
  16. [Yo]
    K.Yosida, Functional Analysis ,Springer-Verlag, New York.Google Scholar

Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • Kazufumi Ito
    • 1
  1. 1.Center for Research in Scientific Computation Department of MathematicsNorth Carolina State UniversityRaleighUSA

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