Visnyk of V.N.Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics

Open access journal                   ISSN 2523-4641 (Online), ISSN 2221-5646 (Print)

Contents and Abstracts

Volume 87, 2018


Ця сторінка Українською / This page in Ukrainian

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O.O. Novikov, O.G. Rovenska, Yu.A. Kozachenko, Approximation of classes of Poisson integrals by Fejer sums. P. 4-12.

For upper bounds of the deviations of Fejer sums taken over classes of periodic functions that admit analytic extensions to a fixed strip of the complex plane, we obtain asymptotic equalities. In certain cases, these equalities give a solution of the corresponding Kolmogorov-Nikolsky problem.

Keywords: asymptotic equality; Poisson integrals; Fejer sums.

2010 Mathematics Subject Classification: 42А10.   [ Full-text available (PDF) ]   Top of the page.

Yu.V. Romashov, E.V. Povolotskii, Influence of the temperature state on the damageability due to the creep of claddings of cylindrical fuel elements. P. 13-28.

This paper deals with the deformation and damageability of the fuel cladding of nuclear reactors, taking into account the creep and the temperature fields across the thickness. Mathematical models and quantitative estimates for durability of the fuel cladding, obtaining using computer simulations, are presented.

Keywords: damageability; creep; fuel cladding; durability; computer simulation.

2010 Mathematics Subject Classification: 74S99; 74R99.   [ Full-text available (PDF) ]   Top of the page.

V.V. Karieva, S.V. Lvov, Mathematical model of liver regeneration processes: homogeneous approximation. P. 29-41.

This paper deals with the rules and the mechanisms regulation of liver regeneration. The generalized mathematical model was developed. This model has an explicit dependence on the control parameters. To solve this problem there were accepted such assumptions: homogeneous approximation; small toxic factors.

Keywords: mathematical model; liver regeneration; homogeneous approximation.

2010 Mathematics Subject Classification: 92C37; 65C20.   [ Full-text available (PDF) ]   Top of the page.

M.V. Goncharenko, L.O. Khilkova, Homogenized conductivity tensor and absorption function of a locally periodic porous medium, P. 42-60.

Short abstract: We consider a problem describing the process of stationary diffusion in a locally-periodic porous medium with nonlinear absorption at the boundary. We base on a work, in which this problem considered in a wider class of perforated domains. We obtain explicit formulas for the effective characteristics of the medium: a conductivity tensor and a function of absorption.

Extended abstract: We study a process of stationary diffusion in locally-periodic porous media with nonlinear absorption at the pore boundary. This process is described by a boundary-value problem for an elliptic equation considered in a complex perforated domain, with a nonlinear third boundary condition on the perforation boundary. In view of the smallness of the local scale of porosity of the media and the complexity of the perforated domain, the direct solution of such boundary-value problems is almost impossible. Therefore, a natural approach in this situation is to study the asymptotic behavior of the solution when the microstructure scale tends to 0, and the transition to the homogenized macroscopic model of the process. Our earlier papers were devoted to homogenization the diffusion equation in a wide class of non-periodically perforated domains: strongly-connected domains, which includes locally-periodically perforated domains. In these works, an homogenized model was obtained, the coefficients of which are expressed in terms of “mesoscopic” (local energy) characteristics of the media, which are determined in small cubes, the size of which, however, are much larger than the microstructure scale. In these papers, convergence theorems were proved under the conditions of the existence of limiting densities of "mesoscopic" characteristics, the fulfillment of which is generally difficult to show, but in a number of specific situations this can be done. In this paper, we show the fulfillment of these conditions and, by studing them, we obtain explicit formulas for the effective characteristics of the locally-periodic porous medium: a conductivity tensor and a function of absorption.

Keywords: homogenization; stationary diffusion; non-linear third boundary value problem; locally periodic porous medium.

2010 Mathematics Subject Classification: 35G65; 35Q80.   [ Full-text available (PDF) ]   Top of the page.

A.A. Makarov, D.A. Levkin, Boundary-value problems in a layer for evolutionary pseudo-differential equations with integral conditions, P. 61-68.

Boundary-value problems for evolutionary pseudo-differential equations with an integral condition are studied. Necessary and sufficient conditions of well-posedness are obtained for these problems in the Schwartz spaces. Existence of a well-posed boundary-value problem is proved for each evolutionary pseudo-differential equation.

Keywords: pseudo-differential equations; boundary-value problem; Fourier transform; Schwartz space.

2010 Mathematics Subject Classification: 35S10.   [ Full-text available (PDF) ]   Top of the page.

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Visnyk Kharkivs'koho natsional'noho universytetu imeni V. N. Karazina, Seriya «Matematyka, prykladna matematyka i mekhanika»

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