On the discretization of topological spaces of block elements with different boundary conditions for cracks of a new type

Authors

  • Babeshko V.A. Kuban State University, Krasnodar, Российская Федерация
  • Kirillova E.V. RheinMain University of Applied Sciences in Wiesbaden, Wiesbaden, Germany
  • Babeshko O.M. Kuban State University, Krasnodar, Российская Федерация
  • Evdokimova O.V. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Российская Федерация
  • Khripkov D.A. Kuban State University, Krasnodar, Российская Федерация
  • Evdokimov V.S. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Российская Федерация
  • Zaretsky A.G. Kuban State University, Krasnodar, Российская Федерация

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-18-4-14-22

Abstract

Block elements of boundary value problems for partial differential equations have a significant set of different properties that are in the process of being studied. Often certain of their properties are revealed by the example of boundary value problems of the same type. Then new properties are revealed, but for a different type of boundary value problems. Naturally, questions arise as to whether these properties belong to both types of boundary value problems, or the exclusion of such a possibility. In this paper, we analyze similar properties related to the discreteness of the topological structure of block elements of boundary problems for different types of boundary conditions, independence from the dimension of the areas of consideration. The issues under consideration are important for modeling cracks of a new type.

Keywords:

boundary value problems, block element method, packed block elements, discrete topological spaces, Helmholtz equation

Acknowledgement

Работа выполнена при поддержке Российского научного фонда (проект 22-29-00213).

Author Infos

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

e-mail: babeshko41@mail.ru

Evgenya V. Kirillova

канд. физ.-мат. наук, профессор Университета прикладных наук Рейн Майн в г. Висбаден

e-mail: kirillova@web.de

Olga M. Babeshko

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

e-mail: babeshko49@mail.ru

Olga V. Evdokimova

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

e-mail: evdokimova.olga@mail.ru

Dmitry A. Khripkov

научный сотрудник Кубанского государственного университета

e-mail: vestnik@fpm.kubsu.ru

Vladimir S. Evdokimov

студент Кубанского государственного университета, лаборант Южного научного центра РАН

e-mail: evdok_vova@mail.ru

Aleksand G. Zaretsky

студент Кубанского государственного университета

e-mail: sam_one@mail.ru

References

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Issue

2021. Vol. 18. No. 4

Section

Mechanics

Pages

14-22

Submitted

2021-12-21

Published

2022-01-10

How to Cite

Babeshko V.A., Kirillova E.V., Babeshko O.M., Evdokimova O.V., Khripkov D.A., Evdokimov V.S., Zaretsky A.G. On the discretization of topological spaces of block elements with different boundary conditions for cracks of a new type. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2021, vol. 18, no. 4, pp. 14-22. DOI: https://doi.org/10.31429/vestnik-18-4-14-22 (In Russian)

Copyright (c) 2022 Babeshko V.A., Kirillova E.V., Babeshko O.M., Evdokimova O.V., Khripkov D.A., Evdokimov V.S., Zaretsky A.G.

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