Skip to main content
SpringerLink
Log in

Optimal identification of coefficients of elliptic equations

  • Data Analysis
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We consider the identification problem for coefficients of a second order elliptic equation. Our basic case is a simple second order elliptic equation. We give a new variational setting of this identification problem, study the correctness of this setting, establish existence and solution regularization theorems, and prove a necessary extremum condition.

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. Lavrent’ev, M.M., Vasil’ev, V.G., and Romanov, V.G., Mnogomernye obratnye zadachi dlya differentsial’nykh uravnenii (Multidimensional Inverse Problems for Differential Equations), Novosibirsk: Nauka, 1969.

    Google Scholar 

  2. Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Solution Methods for Incorrect Problems), Moscow: Nauka, 1979.

    MATH  Google Scholar 

  3. Iskenderov, A.D., On Variational Formulations for Multidimensional Inverse Problems of Mathematical Physics, Dokl. Akad. Nauk USSR, 1984, vol. 274, no. 3, pp. 531–533.

    MathSciNet  Google Scholar 

  4. Iskenderov, A.D., The Inverse Problem for Finding the Coefficients of an Elliptic Equation, Diff. Uravn., 1979, vol. 15, no. 5, pp. 858–867.

    MathSciNet  Google Scholar 

  5. Madatov, M.D., On Problems with Controls in the Coefficients of Elliptic Equations, Mat. Zametki, 1983, vol. 34, no. 6, pp. 973–982.

    MathSciNet  Google Scholar 

  6. Iskenderov, A.D. and Gamidov, R.A., Variational Method for Solving the Inverse Problems for Elliptic Equations with a Special Quality Functional, Vestn. Lenkoran. Gos. Univ., Ser. Est. Nauk, 2007, pp. 57–73.

  7. Gamidov, R.A. and Dzhumshudov, Dzh.S., Variational Method for Finding the Unknown Boundary of a Region in Filtering Problems for Uncompressable Liquids, Mater. nauch. konf. Sovremennye problemy prikl. mat. (Proc. Sci. Conf. Modern Problems of Applied Mathematics), Baku: Bakin. Gos. Univ., 2002, pp. 96–98.

    Google Scholar 

  8. Raitum, U.E., Zadachi optimal’nogo upravleniya dlya ellipticheskikh uravnenii (Optimal Control Problems for Elliptic Equations), Riga: Zinatne, 1989.

    Google Scholar 

  9. Iskenderov, A.D. and Yagubov, G.Ya., Optimal Control of Nonlinear Quantum-Mechanical Systems, Autom. Remote Control, 1989, vol. 50, no. 12, part 1, pp. 1631–1640.

    MATH  MathSciNet  Google Scholar 

  10. Tagiev, R.K., On an Optimal Control Problem for Coefficients of a Second Order Elliptic Equation, Izv. Akad. Nauk Azerb., Ser. Fiz.-Tekh. Mat. Nauk, 1998, vol. 18, no. 2, pp. 88–90.

    MathSciNet  Google Scholar 

  11. 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 

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

    MATH  Google Scholar 

  13. Vasil’ev, F.P., Metody resheniya ekstremal’nykh zadach (Methods for Solving Extremal Problems), Moscow: Nauka, 1981.

    Google Scholar 

  14. Goebel, M., On Existence of Optimal Control, Math. Naehr., 1979, vol. 93, pp. 594–602.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lenkoran State University of the Azerbaijan Republic, Lenkoran, Azerbaijan

    A. D. Iskenderov & R. A. Gamidov

Authors
  1. A. D. Iskenderov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. A. Gamidov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.D. Iskenderov, R.A. Gamidov, 2011, published in Avtomatika i Telemekhanika, 2011, No. 12, pp. 144–155.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Iskenderov, A.D., Gamidov, R.A. Optimal identification of coefficients of elliptic equations. Autom Remote Control 72, 2553–2562 (2011). https://doi.org/10.1134/S0005117911120101

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117911120101

Keywords

Search

Navigation