# Kapustyan V. E.

### Problem of Optimal Control for Parabolic-Hyperbolic Equations with Nonlocal Point Boundary Conditions and Semidefinite Quality Criterion

Kapustyan V. E., Pyshnograev I. A.

Ukr. Mat. Zh. - 2015. - 67, № 8. - pp. 1068-1081

We consider a problem of optimal control for parabolic-hyperbolic equations with nonlocal boundary conditions and semidefinite quality criterion. The optimality conditions are constructed by reducing the problem to a sequence of one-dimensional problems, the optimal control is obtained in a closed form, and its convergence is proved. The form of the quality criterion is substantiated.

### Singularities of Solutions of One Class of Equations of Continuum Mechanics

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 12-21

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.

### Singularities of Solutions of Singular Integral Equations

Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1429-1436

From the point of view of singularities of differential mappings, we determine the dependence between the dimension of a family of singular equations and the types of singularities of their solutions.

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

Ukr. Mat. Zh. - 1996. - 48, № 9. - pp. 1200–1208

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).

### Asymptotics of locally constrained control in optimal parabolic problems

Ukr. Mat. Zh. - 1996. - 48, № 1. - pp. 50-56

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

### The asymptotics of constrained control in optimal singular parabolic problems

Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1345–1355

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.

### Asymptotic analysis of a bounded control in optimal elliptic problems

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1072–1083

An asymptotics of a bounded control is constructed and substantiated for a singularly perturbed optimal elliptic problem.