2019
Том 71
№ 2

All Issues

Feller M. N.

Articles: 13
Article (Russian)

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

Feller M. N., Kovtun I. I.

↓ Abstract   |   Full text (.pdf)

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 hyperbolic equation with divergent part and Levy Laplacian

Feller M. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 2. - pp. 237-244

We propose an algorithm for the solution of the boundary-value problem $U(0,x) = u_0,\;\; U(t, 0) = u_1$ and the external boundary-value problem $U(0, x) = v_0, \;\;U(t, x) |_{\Gamma} = v_1, \;\; \lim_{||x||_H \rightarrow \infty} U(t, x) = v_2$ for the nonlinear hyperbolic equation $$\frac{\partial}{\partial t}\left[k(U(t,x))\frac{\partial U(t,x)}{\partial t}\right] = \Delta_L U(t,x)$$ with divergent part and infinite-dimensional Levy Laplacian $\Delta_L$.

Article (Russian)

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

Feller M. N., Kovtun I. I.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

Boundary-value problems for the wave equation with Lévy Laplacian in the Gâteaux class

Feller M. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 11. - pp. 1564-1574

We present the solutions of the initial-value problem in the entire space and the solutions of the boundary-value and initial-boundary-value problems for the wave equation $$\frac{∂^2U(t,x)}{∂x^2} = Δ_LU(t,x)$$ with infinite-dimensional Lévy Laplacian $Δ_L$ in the class of Gâteaux functions.

Article (Russian)

Notes on infinite-dimensional nonlinear parabolic equations

Feller M. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 5. - pp. 690-701

We present a method for the solution of the Cauchy problem for three broad classes of nonlinear parabolic equations $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {\Delta _L U\left( {t,x} \right)} \right), \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} f\left( {t,\Delta _L U\left( {t,x} \right)} \right),$$ and $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {U\left( {t,x} \right), \Delta _L U\left( {t,x} \right)} \right)$$ with the infinite-dimensional Laplacian ΔL.

Brief Communications (Russian)

The riquier problem for a nonlinear equation unresolved with respect to the Lévy iterated laplacian

Feller M. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 423–427

We present a method of solving for the nonlinear equationf(U(x),Δ L 2 U(x)) = Δ L U(x) (Δ L is an infinite-dimensional Laplacian) unresolved with respect to an iterated infinite-dimensional Laplacian and for the Riquier problem for this equation.

Brief Communications (Russian)

Riquier problem for a nonlinear equation resolved with respect to the iterated Levi Laplacian

Feller M. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1574–1577

Solutions are found for the nonlinear equation Δ L 2 U(x) = f(U(x)) (here, Δ L is an infinite-dimensional Laplacian) which is solved with respect to the iterated infinite-dimensional Laplacian. The Riquier problems are stated for an equation of this sort.

Brief Communications (Russian)

On a nonlinear equation unsolved with respect to the levy laplacian

Feller M. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 719-721

We propose a method for the solution of the nonlinear equationf(U(x),ΔU(x))=F(x) (Δ L is an infinite-dimensional Laplacian, Δ L U(x)=γ, γ≠0) unsolved with respect to the infinite-dimensional Laplacian, and for the solution of the Dirichlet problem for this equation.

Article (Ukrainian)

Necessary and sufficient conditions of harmonicity of functions of infinitely many variables (Jacobian case)

Feller M. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 785–788

A criterion of harmonicity of functions in a Hilbert space is given in the case of weakened mutual dependence of the second derivatives.

Article (Ukrainian)

Supply of harmonic functions of an infinite number of variables. II

Feller M. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 12. - pp. 1687–1693

Article (Ukrainian)

Self-adjointness of a nonsymmetrized infinite-dimensional Laplace-Levy operator

Feller M. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 7. - pp. 997-1001

Article (Ukrainian)

Infinite-dimensional self-adjoint Laplace-Levi operators

Feller M. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 2. - pp. 200—206

Article (Ukrainian)

Infinite-dimensional Laplace-Levi operators

Feller M. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 1. - pp. 69 - 79