2019
Том 71
№ 8

All Issues

Bondarenko V. G.

Articles: 11
Brief Communications (Russian)

Trotter – Daletskii formula for nonlinear disturbance

Bondarenko V. G.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 12. - pp. 1717-1722

For a semilinear parabolic equation, we prove a relation generalizing the Trotter – Daletskii formula.

Article (Russian)

Barrier functions for one class of semilinear parabolic equations

Bondarenko V. G., Prokopenko Yu. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 11. - pp. 1449–1456

For a parabolic quasilinear equation with monotone convex potential, we construct superparabolic and subparabolic barrier functions by the method of decomposition.

Article (Russian)

Jacobi fields on a Riemann manifold

Bondarenko V. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 12. - pp. 1602–1613

Some properties of Jacobi fields on a manifold of nonpositive curvature are considered. As a result, we obtain relations for derivatives of one class of functions on the manifold.

Article (Russian)

Construction of a Fundamental Solution of a Perturbed Parabolic Equation

Bondarenko V. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1011-1021

We propose a method for the construction of a solution of a parabolic equation in the case where the diffusion operator is perturbed.

Brief Communications (Russian)

Perturbed Parabolic Equation on a Riemannian Manifold

Bondarenko V. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 977-982

We construct a fundamental solution of an equation with perturbed diffusion operator on a manifold of nonnegative curvature.

Brief Communications (Russian)

Logarithmic derivatives of diffusion measures in a Hilbert space

Bondarenko V. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 4. - pp. 537-543

For the logarithmic derivative of transition probability of a diffusion process in a Hilbert space, we construct a sequence of vector fields on Riemannian n-dimensional manifolds that converge to this derivative.

Article (Russian)

Finite-dimensional approximations of diffusion measures in a Hilbert space

Bondarenko V. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 12. - pp. 1587–1592

For transition probabilities of diffusion processes in a Hilbert space, we construct finite-dimensional approximations and establish sufficient conditions for the equivalence of such measures under perturbation of the diffusion operator.

Article (Russian)

Parametrix method for a parabolic equation on a Riemannian manifold

Bondarenko V. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1443–1448

We present a scheme of construction of a fundamental solution of a parabolic equation on a Riemannian manifold with nonpositive curvature.

Brief Communications (Ukrainian)

Estimates of the heat kernel on a manifold of nonpositive curvature

Bondarenko V. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 8. - pp. 1129–1136

On a Riemannian manifold of nonpositive curvature, we obtain dimension-independent estimates for the fundamental solution of a parabolic equation and for the logarithmic derivative of this solution.

Article (Russian)

Covariant derivatives of Jacobi fields on a manifold of nonpositive curvature

Bondarenko V. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 6. - pp. 755–764

We obtain estimates of the covariant derivatives of Jacobi fields along a geodesic on a Riemannian manifold of negative curvature.

Article (Ukrainian)

Markov processes in a Hilbert space

Bondarenko V. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1972. - 24, № 2. - pp. 217—219