Bondarenko V. G.
Ukr. Mat. Zh. - 2018. - 70, № 12. - pp. 1717-1722
For a semilinear parabolic equation, we prove a relation generalizing the Trotter – Daletskii formula.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Ukr. Mat. Zh. - 1972. - 24, № 2. - pp. 217—219