Block element method for body, localizations and resonances

Authors

  • Babeshko V.A. Kuban State University, Krasnodar, Российская Федерация
  • Evdokimova O.V. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Российская Федерация
  • Babeshko O.M. Kuban State University, Krasnodar, Российская Федерация
  • Gorshkova E.M. Kuban State University, Krasnodar, Российская Федерация
  • Gladskoi I.B. Kuban State University, Krasnodar, Российская Федерация
  • Grishenko D.V. Kuban State University, Krasnodar, Российская Федерация
  • Telatnikov I.S. Kuban State University, Krasnodar, Российская Федерация

UDC

539.3

Abstract

For isotopic gibbous body deformed in a linear way differential and integral methods of factorization are applied. The algorithm of their usage is shown in details. It consists in submersion of boundary-value problem into topological area with topology induced by spheres of Euclidean space. The studying of the boundary-value problem is conducted in the space of slowly growing generalized functions. With application of means of external analysis the boundary-value problem is lead to the system of functional equations with matrix coefficient. The differential factorization that demanded building factorizing matrix-functions and automorphism allow obtaining pseudodifferential equation. For this purpose the Leray residue form is calculated. The integral equations meeting specific boundary conditions are extracted from it. The method is demonstrated by the example of boundary-value problem for the sphere, from which it is easy to see, that analytical notion of solution allows to reveal localizations and resonant parameter point simply enough.

Keywords:

block element, factorization, spherical ball, integral and differential factorization methods, exterior forms, boundary problems

Acknowledgement

Отдельные фрагменты работы выполнены при поддержке грантов РФФИ (12-01-00330), (12-01-00332), (13-01-96502), (13-01-96505), (13-01-96508), (13-01-96509), (14-08-00404), (13-01-12003)-м, гранта Президента РФ НШ-1245.2014.1, программ отделения ЭММПУ и Президиума РАН, выполняемых Южным научным центром РАН.

Author Infos

Vladimir A. Babeshko

академик РАН, д-р физ.-мат. наук, зав. 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

Elena M. Gorshkova

канд. физ.-мат. наук, старший научный сотрудник Научно-исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета

e-mail: gem@kubsu.ru

Igor B. Gladskoi

канд. физ.-мат. наук, старший научный сотрудник Научно-исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета

e-mail: i.glad@list.ru

Dmitriy V. Grishenko

аспирант кафедры математического моделирования Кубанского государственного университета

e-mail: icmm@fpm.kubsu.ru

Ilya S. Telatnikov

аспирант кафедры математического моделирования Кубанского государственного университета

e-mail: ilux_t@list.ru

References

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Issue

2014. No. 2

Pages

13-19

Submitted

2014-04-15

Published

2014-06-17

How to Cite

Babeshko V.A., Evdokimova O.V., Babeshko O.M., Gorshkova E.M., Gladskoi I.B., Grishenko D.V., Telatnikov I.S. Block element method for body, localizations and resonances. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2014, no. 2, pp. 13-19.

Copyright (c) 2014 Babeshko V.A., Evdokimova O.V., Babeshko O.M., Gorshkova E.M., Gladskoi I.B., Grishenko D.V., Telatnikov I.S.

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