Skip to main content
SpringerLink
Log in

An Approach to Determining the Variation of a Functional with Singularities

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

A new method is proposed for computing the first variation of a functional in the case when the considered domain or its boundary contains singular points. In contrast to earlier proposed techniques, this method is simpler and applies to a larger class of equations governing optimization processes and to more general singularities occurring in the domain or on its boundary.

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. A. N. Kraiko, “On the solution of variational problems of supersonic gas dynamics,” J. Appl. Math. Mech. 30 (2), 381–391 (1966).

    Article  MathSciNet  Google Scholar 

  2. A. V. Shipilin, “Variational gas dynamics problems with attached shock waves,” in Collection of Theoretical Studies on Hydromechanics (Vychisl Tsentr Akad. Nauk SSSR, Moscow, 1970), pp. 54–106 [in Russian].

    Google Scholar 

  3. V. I. Zubov, “Optimal supersonic airfoil of specified thickness,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 89–96 (1976).

  4. A. N. Kraiko, Variational Problems in Gas Dynamics (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  5. V. I. Zubov, “The optimum airfoils at low angles of attack in a supersonic gas flow,” J. Appl. Math. Mech. 61 (1), 83–91 (1997).

    Article  MathSciNet  Google Scholar 

  6. L. C. Young, Lectures on the Calculus of Variations and Optimal Control Theory (Saunders, Philadelphia, 1969).

    MATH  Google Scholar 

  7. N. I. Akhiezer, Lectures on Calculus of Variations (GITTL, Moscow, 1955) [in Russian].

    Google Scholar 

  8. T. K. Sirazetdinov, Optimization of Distributed-Parameter Systems (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  9. Theory of Optimum Aerodynamic Shapes, Ed. by A. Miele (Academic, New York, 1965).

    MATH  Google Scholar 

  10. K. G. Guderley and J. V. Armitage, “A general method for the determination of best supersonic rocket nozzles,” Symposium on Extremal Problems in Aerodynamics (Boeing Scientific Research Laboratories, Flight Science Laboratory, Seattle, Washington, December 3–4, 1962).

  11. T. K. Sirazetdinov, “Optimal problems in gas dynamics,” Izv. Vyssh. Uchebn. Zaved., Ser. Aviats. Tekh., No. 2, 11–21 (1963).

  12. I. M. Gelfand and S. V. Fomin, Calculus of Variations (Fizmatlit, Moscow, 1961; Prentice Hall, Englewood Cliffs, N.J., 1963).

  13. R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves (Interscience, New York, 1948).

    MATH  Google Scholar 

  14. B. L. Roždestvenskii and N. N. Janenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics (Nauka, Moscow, 1978; Am. Math. Soc., Providence, 1983).

  15. L. V. Ovsyannikov, Lectures on Fundamentals of Gas Dynamics (Nauka, Moscow, 1981) [in Russian].

    MATH  Google Scholar 

  16. U. G. Pirumov and G. S. Roslyakov, Gas Dynamics of Nozzles (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

Download references

Funding

This work was supported in part by the Russian Foundation for Basic Research, project no. 17-07-00493a.

Author information

Authors and Affiliations

  1. Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, 119333, Moscow, Russia

    A. F. Albu, Yu. G. Evtushenko & V. I. Zubov

  2. Moscow Institute of Physics and Technology (State University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    A. F. Albu, Yu. G. Evtushenko & V. I. Zubov

Authors
  1. A. F. Albu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. G. Evtushenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. I. Zubov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Zubov.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Albu, A.F., Evtushenko, Y.G. & Zubov, V.I. An Approach to Determining the Variation of a Functional with Singularities. Comput. Math. and Math. Phys. 59, 1215–1232 (2019). https://doi.org/10.1134/S0965542519080025

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542519080025

Keywords:

Search

Navigation