Skip to main content
SpringerLink
Log in

Optimal control for the coefficients of quasilinear parabolic equation with a goal functional on domain boundary

  • Control Theory
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

The optimal control problem for a quasilinear parabolic equation with controls in the coefficients and a goal functional on the domain boundary is considered. The correctness of the statement of the problem is studied and a necessary condition of optimality is derived.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lions, J.-L., Contrôle optimal de systémes gouvernés par des équations aux dérivées partielles, Paris: Dunod, 1968.

    MATH  Google Scholar 

  2. Murat, F., Contre-examples pour divers problems on le controle intervient dans les coefficients, Ann. Mat. Pura Appl., 1977, vol. 112, pp. 49–68.

    Article  MathSciNet  MATH  Google Scholar 

  3. Iskenderov, A.D. and Tagiev, R.K., Problems of optimization with controls in the coefficients of a parabolic equation, Differ. Uravn., 1983, vol. 19, no. 8, pp. 1324–1334.

    MathSciNet  MATH  Google Scholar 

  4. Zolezzi, T., Necessary conditions for optimal control of elliptic or parabolic problems, SIAM J. Control, 1972, vol. 4, no. 2, pp. 594–602.

    Article  MathSciNet  MATH  Google Scholar 

  5. Sokolowski, J., Remarks on existence of solution for parametric optimization problems for partial differential equations of parabolic type, Control Cybernet., 1978, vol. 7, no. 2, pp. 47–61.

    MathSciNet  MATH  Google Scholar 

  6. Serovaiskii, S.Ya., Optimal control problem in the Coefficients of equations of the parabolic type, Izv. Vyssh. Uchebn. Zaved. Mat., 1982, no. 12, pp. 44–50.

    Google Scholar 

  7. Hew, R.J., Optimal control of the convective velocity coefficient in a parabolic equation, Nonlinear Anal., 2005, vol. 63, pp. 1383–1390.

    Article  Google Scholar 

  8. Tagiev, R.K., Optimal coefficient control in parabolic systems, Differ. Equations, 2009, vol. 45, no. 10, pp. 1526–1535.

    Article  MathSciNet  MATH  Google Scholar 

  9. Novozhenov, M.M. and Plotnikov, V.I., The generalized rule of Lagrangian multipliers for distributed systems with phase constraints, Differ. Uravn., 1982, vol. 18, no. 4, pp. 584–592.

    MathSciNet  MATH  Google Scholar 

  10. Novozhenov, M.M. and Sumin, M.I., Optimal control for semilinear parabolic equation with pointwise phase constraint, Vestn. Nizhegor. Gos. Univ., 2001, no. 2, pp. 261–269.

    MATH  Google Scholar 

  11. Tagiev, R.K., Optimal control for the coefficients of a quasilinear parabolic equation, Autom. Remote Control., 2009, vol. 70, no. 11, pp. 1814–1826.

    Article  MathSciNet  Google Scholar 

  12. Tagiev, R.K., Optimal control problem for a quasilinear parabolic equation with controls in the coefficients and with state constraints, Differ. Equations, 2013, vol. 49, no. 3, pp. 369–381.

    Article  MathSciNet  MATH  Google Scholar 

  13. Ladyzhenskaya, O.A., Solonnikov, V.A., and Ural’tseva, N.N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa (Linear and Quasilinear Equations of Parabolic Type), Moscow: Nauka, 1967.

    Google Scholar 

  14. Gajewskii, H., Gröger, K., and Zacharias, K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Berlin: Akademik–Verlag, 1974.

    MATH  Google Scholar 

  15. Lions, J.-L., Upravlenie singulyarnymi raspredelennymi sistemami (Control for Singular Distributed Systems), Moscow, 1987.

    Google Scholar 

  16. Vasil’ev, F.P., Metody resheniya ekstremal’nykh zadach (Methods of Solution for Extremal Problems), Moscow, 1981.

    Google Scholar 

  17. Zabreiko, P.P., Koshelov, A.I., Krasnosel’skii, M.A., et al., Integral’nye uravneniya (Integral Equations), Moscow, 1968.

    Google Scholar 

  18. Ladyzhenskaya, O.A. and Ural’tseva, N.N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa (Linear and Quasilinear Equations of Elliptic Type), Moscow: Nauka, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Baku State University, Baku, AZ1148, Azerbaijan

    R. K. Tagiev

  2. Lankaran State University, Lankaran, AZ4200, Azerbaijan

    R. A. Kasumov

Authors
  1. R. K. Tagiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. A. Kasumov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. K. Tagiev.

Additional information

Original Russian Text © R.K. Tagiev, R.A. Kasumov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 1, pp. 124–134.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tagiev, R.K., Kasumov, R.A. Optimal control for the coefficients of quasilinear parabolic equation with a goal functional on domain boundary. Diff Equat 53, 122–132 (2017). https://doi.org/10.1134/S0012266117010128

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266117010128

Search

Navigation