On a boundary value problem in a wedge-shaped domain

Authors

  • Babeshko V.A. Kuban State University, Krasnodar, Russian Federation
  • Evdokimova O.V. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Russian Federation
  • Babeshko O.M. Kuban State University, Krasnodar, Russian Federation

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-17-1-1-17-22

Abstract

The boundary value problem for the three-dimensional Helmholtz equation is considered in an area that represents a rectangular wedge of infinite length.

The block element method is used for the first time to construct an exact solution of this boundary value problem in the form of a Packed block element, which is necessary for the study of more complex, including mixed problems for block structures. Representations of solutions to boundary problems in the form of Packed block elements make it possible to study and solve boundary problems of almost any complexity and in any areas. This is due to the fact that an arbitrary area can always be represented in real or virtual form as a block structure, blocks of which can be formed from the condition of convenience of solving specified boundary problems on them. In this paper, we consider a three-dimensional Dirichlet boundary value problem for the Helmholtz equation, for which the block element method is used to construct solutions for arbitrary boundary conditions in a wedge-shaped region in the form of Packed and unpacked block elements. There are no such solutions in publications, they exist only for special cases. The block element method solves it quite simply and can be used for more complex tasks.

Keywords:

block element method, boundary value problem, automorphism, pseudo differential equation, wedge-shaped area

Acknowledgement

Отдельные фрагменты работы выполнены в рамках реализации Госзадания Минобрнауки на 2019~г. (проекты 9.8753.2017/8.9), ЮНЦ РАН на 2019 г. (проекта 00-18-04) № госрег. 01201354241, программ президиума РАН I-16 (проект 00-18-21) и I-52 (проект 00-18-29), и при поддержке грантов РФФИ (проекты 19-41-230003, 19-41-230004, 19-48-230014, 17-08-00323, 18-08-00465, 18-01-00384, 18-05-80008).

Author Infos

Vladimir A. Babeshko

академик РАН, д-р физ.-мат. наук, заведующий кафедрой математического моделирования Кубанского государственного университета, директор Научно-исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета, заведующий лабораторией Южного федерального университета

e-mail: babeshko41@mail.ru

Olga V. Evdokimova

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

e-mail: evdokimova.olga@mail.ru

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

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Issue

2020. Vol. 17. No. 1. Part 1

Section

Mechanics

Pages

17-22

Submitted

2020-02-24

Published

2020-03-31

How to Cite

Babeshko V.A., Evdokimova O.V., Babeshko O.M. On a boundary value problem in a wedge-shaped domain. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, vol. 17, no. 1, pp. 17-22. DOI: https://doi.org/10.31429/vestnik-17-1-1-17-22 (In Russian)

Copyright (c) 2020 Babeshko V.A., Evdokimova O.V., Babeshko O.M.

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