2018
Том 70
№ 11

All Issues

Nomirovs'kii D. A.

Articles: 4
Article (Ukrainian)

Generalized solutions for linear operators with weakened a priori inequalities

Anikushyn A. V., Nomirovs'kii D. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1011–1021

We propose an approach to the investigation of generalized solutions of linear operators that satisfy weakened a priori inequalities. This approach generalizes several well-known definitions of generalized solutions of operator equations. We prove existence and uniqueness theorems for a generalized solution.

Article (Ukrainian)

Convergence of the Galerkin method for a wave equation with singular right-hand side

Nomirovs'kii D. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 778–786

We consider analogs of the Galerkin method for a linear wave equation of the fifth order with generalized functions on the right-hand side. Theorems on the convergence of an approximate method, depending on the order of singularity of the right-hand side, are proved.

Article (Russian)

Solvability and Trajectory-Final Controllability of Pseudohyperbolic Systems

Nomirovs'kii D. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 3. - pp. 366–376

We consider the problem of solvability and optimization for a pseudohyperbolic operator of the general form. We prove theorems on existence and uniqueness for various right-hand sides of the equation. The results obtained are applied to the problem of trajectory-final controllability.

Brief Communications (Russian)

On Homeomorphisms Realized by Certain Partial Differential Operators

Nomirovs'kii D. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1707-1716

For a sufficiently broad class of partial differential operators, we prove a theorem on homeomorphisms. Applications of this theorem to some classical operators are considered.