Skip to main content
Log in

Solvability of stationary boundary control problems for heat convection equations

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  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. 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).

    MathSciNet  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  4. J.-L. Lions Control of Singular Distributed Systems [Russian translation], Nauka, Moscow (1987).

    Google Scholar 

  5. F. Abergel, and R. Temam, “On some control problems in fluid mechanics,” Theoret. Comput. Fluid Dynamics,1, 303–325 (1990).

    Article  MATH  Google Scholar 

  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).

    MATH  Google Scholar 

  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).

    MATH  Google Scholar 

  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).

    Article  MATH  MathSciNet  Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

  10. M. Desai and K. Ito, “Optimal controls of Navier-Stokes equations,” SIAM J. Control Optim.,32, No. 5, 1428–1446 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  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. 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).

    Article  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  15. A. D. Ioffe, and V. M. Tikhomirov, “The Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  16. O. A. Ladyzhenskaya, Mathematical Questions of the Dynamics of a Viscous Incompressible Fluid [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  17. R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis [Russian translation], Mir, Moscow (1981).

    MATH  Google Scholar 

  18. V. Girault, and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, New York (1986).

    MATH  Google Scholar 

  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. V. I. Yudovich, “Free convection and branching,” Prikl. Mat. Mekh.,31, No. 1, 101–111 (1967).

    MATH  Google Scholar 

  21. A. G. Zarubin, “A problem of free stationary convection,” Zh. Vychisl. Mat. i Mat. Fiz.,8, No. 6, 1378–1383 (1968).

    MATH  MathSciNet  Google Scholar 

  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. 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).

    MATH  MathSciNet  Google Scholar 

Download references

Authors

Additional information

The research was supported by the Competition Center for Basic Natural Sciences at St. Petersburg State University (Grant 95-0-4.2-97).

Vladivostok. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 39, No. 5, pp. 982–998, September–October, 1998.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alekseev, G.V. Solvability of stationary boundary control problems for heat convection equations. Sib Math J 39, 844–858 (1998). https://doi.org/10.1007/BF02672906

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02672906

Keywords

Navigation

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy