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Siberian Mathematical Journal

, Volume 39, Issue 5, pp 844–858 | Cite as

Solvability of stationary boundary control problems for heat convection equations

  • G. V. Alekseev
Article

Keywords

Control Problem Lagrange Multiplier Optimal Control Problem Extremal Problem Boundary Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    V. K. Andreev, O. V. Kaptsov, V. V. Pukhnachëv, and A. A. Rodionov, Application of the Group-Theoretic Methods to Hydrodynamics [in Russian], Nauka, Novosibirsk (1994).Google Scholar
  2. 2.
    A. V. Fursikov, “Control problems and theorems related to unique solvability of a mixed boundary value problem for the three-dimensional Navier-Stokes and Euler equations,” Mat. Sb.,115, No. 2, 281–306 (1981).MathSciNetGoogle Scholar
  3. 3.
    A. V. Fursikov, “Properties of solutions to some extremal problems related to the Navier-Stokes system,” Mat. Sb.,118, No. 3, 323–349 (1982).MathSciNetGoogle Scholar
  4. 4.
    J.-L. Lions Control of Singular Distributed Systems [Russian translation], Nauka, Moscow (1987).Google Scholar
  5. 5.
    F. Abergel, and R. Temam, “On some control problems in fluid mechanics,” Theoret. Comput. Fluid Dynamics,1, 303–325 (1990).zbMATHCrossRefGoogle Scholar
  6. 6.
    M. D. Gunzburger, L. Hoo, and T. P. Svobodny, “Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls,” Math. Comput.,57, No. 195, 123–151 (1991).zbMATHGoogle Scholar
  7. 7.
    M. D. Gunzburger, L. Hoo, and T. P. Svobodny, “Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls,” Math. Modelling Numer. Anal.,25, No. 6, 711–748 (1991).zbMATHGoogle Scholar
  8. 8.
    M. D. Gunzburger, L. Hoo, and T. P. Svobodny “Boundary velocity control of incompressible flow with an application to viscous drag reduction,” SIAM J. Control Optim.,30, No. 1, 167–181 (1992).zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    F. Abergel, and F. Casas, “Some optimal control problems of multistate equations appearing in fluid mechanics,” Math. Modelling Numer. Anal.,27, 223–247 (1993)zbMATHMathSciNetGoogle Scholar
  10. 10.
    M. Desai and K. Ito, “Optimal controls of Navier-Stokes equations,” SIAM J. Control Optim.,32, No. 5, 1428–1446 (1994).zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    G. V. Alekseev, and V. V. Malykin “Numerical study of stationary extremal problems for two-dimensional equations of a viscous fluid,” Vychislitel'nye Tekhnologii,2, No. 5, 5–16 (1993).Google Scholar
  12. 12.
    G. V. Alekseev, and V. V. Malikin, “Numerical analysis of optimal boundary control problems for Navier-Stokes equations,” Comp. Fluid Dynamics J.,3, No. 1, 1–26 (1994).CrossRefGoogle Scholar
  13. 13.
    A. Yu. Chebotarëv, “Extremal boundary value problems of the dynamics of a viscous incompressible fluid,” Sibirsk. Mat. Zh.,34, No. 5, 202–213 (1993).MathSciNetGoogle Scholar
  14. 14.
    A. Yu. Chebotarëv, “Normal solutions to boundary value problems for stationary systems of the Navier-Stokes type,” Sibirsk. Mat. Zh.,36, No. 4, 934–942 (1995).MathSciNetGoogle Scholar
  15. 15.
    A. D. Ioffe, and V. M. Tikhomirov, “The Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).Google Scholar
  16. 16.
    O. A. Ladyzhenskaya, Mathematical Questions of the Dynamics of a Viscous Incompressible Fluid [in Russian], Nauka, Moscow (1970).Google Scholar
  17. 17.
    R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis [Russian translation], Mir, Moscow (1981).zbMATHGoogle Scholar
  18. 18.
    V. Girault, and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, New York (1986).zbMATHGoogle Scholar
  19. 19.
    M. R. Ukhovskiî and V. I. Yudovich, “On the equations of stationary convection,”Prikl. Mat. Mekh.,27, No. 2, 295–300 (1963).Google Scholar
  20. 20.
    V. I. Yudovich, “Free convection and branching,” Prikl. Mat. Mekh.,31, No. 1, 101–111 (1967).zbMATHGoogle Scholar
  21. 21.
    A. G. Zarubin, “A problem of free stationary convection,” Zh. Vychisl. Mat. i Mat. Fiz.,8, No. 6, 1378–1383 (1968).zbMATHMathSciNetGoogle Scholar
  22. 22.
    G. V. Alekseev, Theoretic Analysis of Stationary Boundary Control Problems for Equations of Heat Convection [Preprint/ IPM DVO RAN]] [in Russian], Dal'Nauka, Vladivostok (1996).Google Scholar
  23. 23.
    R. Finn, and V. Solonnikov, “Gradient estimates for solutions of the Navier-Stokes equations,” Topol. Methods in Nonlinear Anal., J. Juliusz Schauder Center,9, No. 1, 29–39 (1997).zbMATHMathSciNetGoogle Scholar

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© Plenum Publishing Corporation 1998

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  • G. V. Alekseev

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