Global Attractor for a Nonautonomous Inclusion with Discontinuous Right-Hand Side

We consider a nonautonomous inclusion the upper and lower selectors of whose right-hand side are determined by functions with discontinuities of the first kind. We prove that this problem generates a family of multivalued semiprocesses for which there exists a global attractor compact in the phase space.     

Optimal control over the heat field in thin bodies local constraints on control

Asymptotic solutions of problems of optimal locally constrained control over the heat field in thin bodies are constructed and justified. These problems relate to the critical case of singularly perturbed systems (the degenerate problem has a family of solutions). Dnepropetrovsk Technical University of Railway Transport, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9, pp. 1200–1208, September, 1996.     

Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system

In this paper we construct a dynamical process (in general, multivalued) generated by the set of solutions of an optimal control problem for the three-dimensional Navier-Stokes system. We prove the existence of a pullback attractor for such multivalued process. Also, we establish the existence of a uniform global attractor containing the pullback attractor. Moreover, under the unproved assumption that strong globally defined solutions of the three-dimensional Navier-Stokes system exist, which guaranties the existence of a global attractor for the corresponding multivalued semiflow, we show that the pullback attractor of the process coincides with the global attractor of the semiflow.     

Asymptotics of locally constrained control in optimal parabolic problems

We construct and justify asymptotic solutions of optimal parabolic problems with locally constrained control which depends only on time.     

Approximate Averaged Synthesis of the Problem of Optimal Control for a Parabolic Equation

For a problem of optimal control for a parabolic equation, in the case of bounded control, we construct and justify an approximate averaged control in the form of feedback.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1384–1394, October, 2004.     

Asymptotic analysis of a bounded control in optimal elliptic problems

An asymptotics of a bounded control is constructed and substantiated for a singularly perturbed optimal elliptic problem.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 8, pp. 1072–1083, August, 1993.     

The asymptotics of constrained control in optimal singular parabolic problems

A complete asymptotic solution is constructed and justified for the optimal singular parabolic problems with constrained control and a completely degenerate differential part of an operator.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1345–1355, October, 1993.