2019
Том 71
№ 9

Kovtun I. I.

Articles: 4
Article (Russian)

Boundary-value problems for a nonlinear hyperbolic equation with Levy Laplaciana

Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1492-1499

We present solutions of the boundary-value problem $U(0, x) = u_0, \;U(t, 0) = u_1$, and the external boundary-value problem $U(0, x) = v_0,\; U(t, x)|_{Γ} = v_1,\; \lim_{||x||_H→∞} U(t, x) = v_2$ for the nonlinear hyperbolic equation $$\frac{∂^2U(t, x)}{∂t^2} + α(U(t, x)) \left[\frac{∂U(t, x)}{∂t}\right]^2 = ∆_LU(t, x)$$ with infinite-dimensional Levy Laplacian $∆_L$.

Article (Russian)

Boundary-value problems for a nonlinear parabolic equation with Lévy Laplacian resolved with respect to the derivative

Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1400–1407

We present the solutions of boundary-value and initial boundary-value problems for a nonlinear parabolic equation with Lévy Laplacian $∆_L$ resolved with respect to the derivative $$\frac{∂U(t,x)}{∂t}=f(U(t,x),Δ_LU(t,x))$$ in fundamental domains of a Hilbert space.

Brief Communications (Russian)

Fluctuations of forced vibrations in a medium with resistance

Ukr. Mat. Zh. - 1993. - 45, № 1. - pp. 132–135

For a differential oscillation equation with coefficients perturbed by Gaussian delta-correlated random processes with a random external force, we obtain closed moment equations. In a special case, the mathematical expectation and the covariance function are found.

Brief Communications (Russian)

On the asymptotic solution of a linear operator differential equation

Ukr. Mat. Zh. - 1962. - 14, № 2. - pp. 205-211