Skip to main content
SpringerLink
Log in

Optimal control problem for the backward heat equation

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

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

References

  1. M. M. Lavrent'ev, V. G. Romanov, and S. P. Shishatskiî, Ill-Posed Problems of Mathematical Physics and Analysis [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  2. A. V. Fursikov, “On some control problems and on results related to unique solvability of a mixed boundary value problem for the Navier-Stockes and Euler three-dimensional systems,” Dokl. Akad. Nauk SSSR,252, No. 5, 1066–1070 (1980).

    Google Scholar 

  3. A. V. Fursikov, “Control problems and theorems related to unique solvability of a mixed boundary value problem for the three-dimensional Navier-Stockes and Euler systems,” Mat. Sb.,115, No. 2, 281–307 (1981).

    Google Scholar 

  4. A. V. Fursikov, “Properties of solutions to some extremal problems connected with the Navier-Stockes systems,” Mat. Sb.,118, No. 3, 323–349 (1982).

    Google Scholar 

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

    Google Scholar 

  6. P. H. Rivera, “Optimal control of unstable nonlinear, evolution systems,” Ann. Fac. Sci. Toulouse Math., No. 1, 33–50 (1984).

    Google Scholar 

  7. P. N. Rivera and C. F. Vasconcellos, “Optimal control for a backward parabolic system,” SIAM J. Control Optim.,25, No. 5, 1163–1172 (1987).

    Google Scholar 

  8. A. V. Fursikov, “Lagrange principle for problems of optimal control of ill-posed or distributed systems,” J. Math. Pures Appl.,71, No. 2, 1–57 (1992).

    Google Scholar 

  9. D. L. Russel, “Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions,” SIAM Rev.,20, No. 4, 639–739 (1978).

    Google Scholar 

  10. G. Schmidt, “Even more states reachable by boundary control for the heat equation,”, SIAM J. Control Optim.,24, No. 6, 1319–1322 (1986).

    Google Scholar 

  11. J. L. Lions, Ouelque Méthodes de Résolution des Problemes aux Limites non Linéaires [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  12. J. L. Lions and E. Magenes, Problems aux Limites non Homogenes et Applications. Vol. 2, Dunod, Paris (1968).

    Google Scholar 

  13. V. A. Solonikov, “A priori estimates for second order equations of parabolic type,” Trudy Mat. Inst. Steklov,70, 133–212 (1966).

    Google Scholar 

Download references

Authors
  1. O. Yu. Èmanuilov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Moscow. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 1, pp. 204–211, January–February, 1993.

Translated by G. V. Dyatlov

Rights and permissions

Reprints and permissions

About this article

Cite this article

Èmanuilov, O.Y. Optimal control problem for the backward heat equation. Sib Math J 34, 181–188 (1993). https://doi.org/10.1007/BF00971254

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00971254

Keywords

Search

Navigation