On systems of integral equations with a difference kernel

Authors

  • Babeshko V.A. Kuban State University, Stavropolskaya str., 149, Krasnodar, 350040, Russian Federation ORCID iD 0000-0002-6663-6357
  • Babeshko O.M. Kuban State University, Stavropolskaya str., 149, Krasnodar, 350040, Russian Federation ORCID iD 0000-0003-1869-5413
  • Evdokimova O.V. Federal Research Centre the Southern Scientific Centre of the Russian Academy of Sciences, Prospekt Chekhova, 41, Rostov-on-Don, Russian Federation ORCID iD 0000-0003-1283-3870
  • Khripkov D.A. Kuban State University, Stavropolskaya str., 149, Krasnodar, 350040, Russian Federation ORCID iD 0000-0002-2161-121X
  • Uafa G.N. Federal Research Centre the Southern Scientific Centre of the Russian Academy of Sciences, Prospekt Chekhova, 41, Rostov-on-Don, 344006, Russian Federation
  • Lozovoy V.V. Federal Research Centre the Southern Scientific Centre of the Russian Academy of Sciences, Prospekt Chekhova, 41, Rostov-on-Don, 344006, Russian Federation ORCID iD 0000-0002-2626-6080
  • Pluzhnik A.V. Federal Research Centre the Southern Scientific Centre of the Russian Academy of Sciences, Prospekt Chekhova, 41, Rostov-on-Don, 344006, Russian Federation

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-19-1-42-44

Abstract

A number of mixed problems of continuum mechanics and mathematical physics are reduced to solving systems of integral equations, whose kernels have singular or logarithmic features. In the case when a layered medium is considered, the kernels of integral equations depend on the difference of arguments. Such systems of integral equations include the Wiener-Hopf equations. The paper develops a method for studying such systems of integral equations, which is based on a method developed for the case of a system consisting of two equations. When studying a number of similar problems for systems of integral equations of finite number, it is sufficient to represent the general form of each component of the solution. A general representation of the solution of such a system of integral equations is given. It can serve the purposes of studying the types of stress concentration at the edges of its research area.

Keywords:

systems of integral equations, meromorphic functions, factorization, general form of solution

Funding information

Some fragments of the work were carried out as part of the implementation of the State task for 2022 of Ministry of Education and Science of Russia (project FZEN-2020-0020), Southern Scientific Center of Russian Academy of Science (project 00-20-13) State Registration No. 122020100341-0, and with the support of the Russian Foundation for Basic Research grants (projects 19-41-230003, 19-41-230004, 19-48-230014).

Author info

  • Vladimir A. Babeshko

    академик РАН, д-р физ.-мат. наук, заведующий кафедрой математического моделирования Кубанского государственного университета, руководитель научных направлений математики и механики Южного научного центра РАН

  • Olga M. Babeshko

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

  • Olga V. Evdokimova

    д-р физ.-мат. наук, главный научный сотрудник Южного научного центра РАН

  • Dmitry A. Khripkov

    научный сотрудник Кубанского государственного университета

  • Galina N. Uafa

    инженер-исследователь Южного научного центра РАН

  • Viktor V. Lozovoy

    канд. физ.-мат. наук, научный сотрудник Южного научного центра РАН

  • Andrey V. Pluzhnik

    младший научный сотрудник Южного научного центра РАН

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Issue

Vol. 19 (2022) No. 1

Pages

42-44

Section

Mechanics

Dates

Submitted

February 24, 2022

Accepted

March 7, 2022

Published

March 30, 2022

How to Cite

[1]
Babeshko, V.A., Babeshko, O.M., Evdokimova, O.V., Khripkov, D.A., Uafa, G.N., Lozovoy, V.V., Pluzhnik, A.V., On systems of integral equations with a difference kernel. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2022, т. 19, № 1, pp. 42–44. DOI: 10.31429/vestnik-19-1-42-44

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Copyright (c) 2022 Бабешко В.А., Бабешко О.М., Евдокимова О.В., Хрипков Д.А., Галина Николаевна У., Лозовой В.В., Плужник А.В.

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