Skip to main content
Log in

Some questions in the theory of the optimal control of nonlinear distributed parameter systems

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Literature cited

  1. J.-L. Lions, Sur le ContrÔle Optimal des Systèmes Gouvernés par des équations aux Derivees Partielles, Dunod, Gauthier-Villars, Paris (1968).

    Google Scholar 

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

    Google Scholar 

  3. A. V. Fursikov, “Control problems and theorems on the unique solvability of a mixed boundary-value problem for three-dimensional Navier-Stokes and Euler systems,” Mat. Sb.,115, (157), No. 2(6), 287–307 (1981).

    Google Scholar 

  4. A. V. Fursikov, “Properties of solutions of certain control problems connected with a Navier-Stokes system,” Dokl. Akad. Nauk SSSR,262, No. 1, 44–48 (1982).

    Google Scholar 

  5. A. V. Fursikov, “Properties of solutions of certain extremal problems connected with a Navier-Stokes system,” Mat. Sb.,118 (160), No, 3(7), 323–349 (1982).

    Google Scholar 

  6. N. V. Efimov and S. B. Stechkin, “Approximate compactness and Chebyshev sets,” Dokl. Akad. Nauk SSSR,140, No. 3, 522–524 (1961).

    Google Scholar 

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

    Google Scholar 

  8. J.-L. Lions, Optimal Control of Non-Well-Posed Distributed Systems, INRIA (1980).

  9. J.-L. Lions, On the Optimal Control of Unstable Distributed Systems, College de France and INRIA (1981).

  10. S. B. Stechkin, “Approximate properties of sets in normed linear spaces,” Rev. Math. Pure Appl.,8, No. 1, 5–18 (1963).

    Google Scholar 

  11. I. Ekeland and R. Temam, Analyse Convexe et Problèmes Variationnels, Dunod, Paris (1973).

    Google Scholar 

  12. J.-L. Lions and E. Magenes, Problèmes aux Limites Non Homogènes et Applications, Vols. 1–3, Dunod, Paris (1968) (Vols.1, 2) (1970) (Vol. 3).

    Google Scholar 

  13. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam-New York (1978).

    Google Scholar 

  14. C. Foias and R. Temam, “Structure of the set of stationary solutions of the Navier-Stokes equations,” Commun. Pure Appl. Math.,30, No. 2, 149–164 (1977).

    Google Scholar 

  15. J.-L. Lions, Some Methods of Solving Nonlinear Boundary Value Problems [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  16. M. I. Vishik and A. V. Fursikov, Mathematical Problems in Statistical Hydromechanics [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  17. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc. (1968).

  18. A. G. Kurosh, A Course of Higher Algebra [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  19. J.-L. Lions, “The optimal control of distributed systems,” Usp. Mat. Nauk,28, No. 4, 15–46 (1973).

    Google Scholar 

Download references

Authors

Additional information

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 9, pp. 167–189, 1983.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fursikov, A.V. Some questions in the theory of the optimal control of nonlinear distributed parameter systems. J Math Sci 33, 1292–1310 (1986). https://doi.org/10.1007/BF01084753

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01084753

Keywords

Navigation