Kapustyan V. E.
Problem of Optimal Control for Parabolic-Hyperbolic Equations with Nonlocal Point Boundary Conditions and Semidefinite Quality Criterion
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.
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.
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.
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).
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.
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.
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.