Journal of Mathematical Sciences

, Volume 174, Issue 2, pp 159–168 | Cite as

A parabolic boundary-value problem and a problem of optimal control

  • I. D. Pukalskyi

We establish necessary and sufficient conditions for the choice of optimal control of systems described by a parabolic boundary-value problem with restricted internal and boundary controls. The criterion of quality is represented as a sum of volume and surface integrals.


Optimal Control Problem Boundary Control Parabolic Type Exterior Domain Landau Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. M. Vigak, Control of Temperature Stresses and Displacements [in Russian], Naukova Dumka, Kiev (1988).Google Scholar
  2. 2.
    G. Duvaut and J. L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris (1972).MATHGoogle Scholar
  3. 3.
    S. D. Ivasyshen, Green Matrices of General Inhomogeneous Boundary Problems for Systems Parabolic by Petrovskii [in Russian], Preprint, Institute of Mathematics, Academy of Sciences of Ukr. SSR, Kyiv (1968).Google Scholar
  4. 4.
    V. A. Il’in and E. I. Moiseev, “Optimization of the control of elastic boundary forces at two ends of a string for an arbitrary sufficiently long time interval T ,” Dokl. Ross. Akad. Nauk, 417, No. 4, 456–463 (2007).Google Scholar
  5. 5.
    J. L. Lions, Contrôle Optimal de Systèmes Gouvernées par des Equations aux Dérivées Partielles, Dunod, Paris (1971).Google Scholar
  6. 6.
    K. A. Lur’e, Optimal Control in Problems of Mathematical Physics [in Russian], Nauka, Moscow (1975).Google Scholar
  7. 7.
    M. I. Matiichuk, Parabolic and Elliptic Problems with Singularities [in Ukrainian], Prut, Chernivtsi (2003).Google Scholar
  8. 8.
    S. D. Eidelman, S. D. Ivasyshen, and A. N. Kochubei, Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type, Birkhäuser, Basel (2004).MATHGoogle Scholar
  9. 9.
    M. Majewski, “On the existence of optimal solutions to an optimal control problem,” J. Optimiz. Theory Appl., 126, No. 3, 635–651 (2006).MathSciNetCrossRefGoogle Scholar
  10. 10.
    A. Rösch and F. Tröltzsch, “Existence of regular Lagrange multipliers for a nonlinear elliptic optimal control problem with pointwise control-state constraints,” SIAM J. Contr. Optimiz., 45, No. 2, 548–564 (2006).CrossRefGoogle Scholar
  11. 11.
    G. Wang, L. Wang, and D. Yang, “Shape optimization of an elliptic equation in an exterior domain,” SIAM J. Contr. Optimiz., 45, No. 2, 532–547 (2006).CrossRefGoogle Scholar
  12. 12.
    Y. Kou and Sh. Ding, “Solutions of Ginzburg–Landau equations with weight and minimizers of the renormalized energy,” Appl. Math. J. Chin. Univ., Ser. B, 22, No. 1, 48–60 (2007).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • I. D. Pukalskyi
    • 1
  1. 1.Fed’kovych Chernivtsi UniversityChernivtsiUkraine

Personalised recommendations