Skip to main content
SpringerLink
Log in

Extremal solutions of certain operator-differential systems

  • Published:
Ukrainian Mathematical Journal Aims and scope

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

Literature cited

  1. V. I. Ivanenko and V. S. Mel'nik, Variational Methods in Control Problems for Systems with Distributed Parameters [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

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

    Google Scholar 

  3. A. V. Fursikov, “Properties of solutions of certain extremal problems connected with the Navier-Stokes system,” Mat. Sb.,118, No. 3, 323–349 (1982).

    Google Scholar 

  4. V. I. Ivanenko and V. S. Mel'nik, “The method of monotonous operators in control problems for quasilinear systems,” Kibernetika, No. 2, 63–67 (1988).

    Google Scholar 

  5. U. Mackenroth, “On parabolic distributed optimal control problems with restriction on the gradient,” Appl. Math. Optim.,10, No. 1, 69–95 (1983).

    Google Scholar 

  6. P. Neittaanmaki and D. Tiba, “A variational inequality approach to constrined control problems for parabolic equations,” Appl. Math. Optim.,17, No. 3, 185–201 (1988).

    Google Scholar 

  7. V. K. Kalantarov and O. A. Ladyzhenskaya, “Collapse phenomena for quasilinear equations of parabolic and hyperbolic types,” Zap. Nauch. Sem. Len. Otdel. Mat. Inst., Academy of Sciences of the SSSR,69, 77–102 (1977).

    Google Scholar 

  8. V. A. Galaktionov, “Conditions for the absence of global solutions of a class of quasilinear parabolic solutions,” Zh. Vychish. Mat. Mat. Fiz.,22, No. 2, 322–338 (1982).

    Google Scholar 

  9. V. S. Mel'nik, “Extremal problems for evolution equations with operator constraints,” Dokl. Akad. Nauk SSSR, Ser. A, No. 3, 72–75 (1989).

    Google Scholar 

  10. V. I. Ivanenko and V. S. Mel'nik, “Optimal control of evolution equations with multivalued operators,” Dokl. Akad. Nauk SSSR,297, No. 6, 1010–1013 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Cybernetics, Academy of Sciences of the Ukrainian SSR, Kiev

    V. S. Mel'nik

Authors
  1. V. S. Mel'nik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 11, pp. 1494–1501, November, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mel'nik, V.S. Extremal solutions of certain operator-differential systems. Ukr Math J 41, 1285–1291 (1989). https://doi.org/10.1007/BF01056496

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01056496

Keywords

Search

Navigation