On transformations of systems of integral equations for a multicomponent nano particle lying on a deformable layer under vibration conditions

Authors

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-19-4-27-36

Abstract

In the work, by applying a universal modeling method, the systems of Wiener-Hopf integral equations are reduced to infinite systems of linear algebraic equations. Systems of Wiener-Hopf integral equations of finite order arise in mixed problems of continuum mechanics for modeling multicomponent nanoparticles on a layered deformable medium of finite thickness. Galerkin transformations are carried out, which turn out to be possible due to the fact that the matrix-function of the transformation of the kernel of the system of integral equations has meromorphic elements. As a result of transformations, the system of integral equations is reduced to infinite systems of linear algebraic equations, the research methods and solutions of which are developed by the authors and will be applied to the constructed infinite systems of algebraic equations.

Keywords:

multicomponent nanoparticles, systems of integral equations, Galerkin transformations

Funding information

The work was supported by the Russian Science Foundation (project 22-21-00128).

Author info

  • Vladimir A. Babeshko

    академик РАН, д-р физ.-мат. наук, заведующий кафедрой математического моделирования Кубанского государственного университета

  • Olga V. Evdokimova

    д-р физ.-мат. наук, главный научный сотрудник научно-исследовательской части Кубанского государственного университета

  • Olga M. Babeshko

    д-р физ.-мат. наук, главный научный сотрудник научно-исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета

  • Marina V. Zaretskaya

    д-р физ.-мат. наук, профессор кафедры математического моделирования Кубанского государственного университета

  • Ilya S. Telyatnikov

    канд. физ.-мат. наук, научный сотрудник научно-исследовательской части Кубанского государственного университета

  • Dmitry A. Snetkov

    инженер Научно-исследовательской части Кубанского государственного университета

  • Olga A. Grishko

    студентка магистратуры факультета компьютерных технологий и математики Кубанского государственного университета

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Issue

Vol. 19 (2022) No. 4

Pages

27-36

Section

Mechanics

Dates

Submitted

November 15, 2022

Accepted

November 16, 2022

Published

November 30, 2022

How to Cite

[1]
Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., Zaretskaya, M.V., Telyatnikov, I.S., Snetkov, D.A., Grishko, O.A., On transformations of systems of integral equations for a multicomponent nano particle lying on a deformable layer under vibration conditions. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2022, т. 19, № 4, pp. 27–36. DOI: 10.31429/vestnik-19-4-27-36

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Copyright (c) 2022 Бабешко В.А., Евдокимова О.В., Бабешко О.М., Зарецкая М.В., Телятников И.С., Снетков Д.А., Гришко О.А.

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