http://dspace.nbuv.gov.ua:80/handle/123456789/140538 2026-04-18T21:57:50Z 2026-04-18T21:57:50Z http://dspace.nbuv.gov.ua:80/handle/123456789/140571 2018-07-10T22:23:29Z 2017-01-01T00:00:00Z

Евгений Яковлевич Хруслов (к восьмидесятилетию со дня рождения) 7 января 2017 г. исполнилось 80 лет замечательному математику, академику НАН Украины, президенту Харьковского математического общества, одному из основателей современной математической теории усреднения Евгению Яковлевичу Хруслову.

2017-01-01T00:00:00Z Levchuk, V.N. http://dspace.nbuv.gov.ua:80/handle/123456789/140570 2018-07-10T22:23:28Z 2017-01-01T00:00:00Z

On One Class of Non-Dissipative Operators Levchuk, V.N. The non-dissipative operator of integration is studied in the weight space. Its similarity to the operator of integration in the space without weight is proved. The functional model for this operator is obtained.

2017-01-01T00:00:00Z Goncharenko, M. Khilkova, L. http://dspace.nbuv.gov.ua:80/handle/123456789/140569 2018-07-10T22:23:26Z 2017-01-01T00:00:00Z

Homogenized Model of Non-Stationary Diffusion in Porous Media with the Drift Goncharenko, M.; Khilkova, L. We consider an initial boundary-value problem for a parabolic equation describing non-stationary diffusion in porous media with non-linear absorption on the boundary and the transfer of the diffusing substance by fluid. We prove the existence of the unique solution for this problem. We study the asymptotic behavior of a sequence of solutions when the scale of microstructure tends to zero and obtain the homogenized model of the diffusion process.

2017-01-01T00:00:00Z Filipkovska, M.S. Kotlyarov, V.P. Melamedova, E.A. http://dspace.nbuv.gov.ua:80/handle/123456789/140568 2018-07-10T22:23:23Z 2017-01-01T00:00:00Z

Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems Filipkovska, M.S.; Kotlyarov, V.P.; Melamedova, E.A. A mixed initial-boundary value problem for nonlinear Maxwell{Bloch (MB) equations without spectral broadening is studied by using the inverse scattering transform in the form of the matrix Riemann{Hilbert (RH) problem. We use transformation operators whose existence is closely related with the Goursat problems with nontrivial characteristics. We also use a gauge transformation which allows us to obtain Goursat problems of the canonical type with rectilinear characteristics, the solvability of which is known. The transformation operators and a gauge transformation are used to obtain the Jost type solutions of the Ablowitz-Kaup-Newel-Segur equations with well-controlled asymptotic behavior by the spectral parameter near singular points. A well posed regular matrix RH problem in the sense of the feasibility of the Schwartz symmetry principle is obtained. The matrix RH problem generates the solution of the mixed problem for MB equations.

2017-01-01T00:00:00Z