The Class of Solenoidal Planar-Helical Vector Fields
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The Class of Solenoidal Planar-Helical Vector Fields
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| Автор |
Vereshchagin, V. P.
Subbotin, Y. N. Chernykh, N. I. |
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| Тематика |
CURL
GROMEKA'S PROBLEM SCALAR FIELDS TENSOR FIELDS VECTOR FIELDS WAVELETS |
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| Описание |
The class of solenoidal vector fields whose lines lie in planes parallel to R2 is constructed by the method of mappings. This class exhausts the set of all smooth planarhelical solutions of Gromeka's problem in some domain D ⊂ R3. In the case of domains D with cylindrical boundaries whose generators are orthogonal to R2, it is shown that the choice of a specific solution from the constructed class is reduced to the Dirichlet problem with respect to two functions that are harmonic conjugates in D2 = D∩R2; i.e., Gromeka's nonlinear problem is reduced to linear boundary value problems. As an example, a specific solution of the problem for an axisymmetric layer is presented. The solution is based on solving Dirichlet problems in the form of series uniformly convergent in D̄2 in terms of wavelet systems that form bases of various spaces of functions harmonic in D2. © 2011 Pleiades Publishing, Ltd.
Российский Фонд Фундаментальных Исследований (РФФИ): 09-01-00014 Ural Branch, Russian Academy of Sciences Russian Academy of Sciences This work was supported by the Russian Foundation for Basic Research (project no. 09-01-00014) and by the Ural Branch of the Russian Academy of Sciences under the Program of the Presidium of the Russian Academy of Sciences “Mathematical Theory of Control.” |
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| Дата |
2019-07-17T10:00:05Z
2019-07-17T10:00:05Z 2011 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
0081-5438
1531-8605 https://www.scopus.com/record/display.uri?origin=resultslist&eid=2-s2.0-79959273501 https://elar.rsvpu.ru/handle/123456789/28028 10.1134/S008154381105018X 79959273501 2-s2.0-79959273501 Russian State Professional-Pedagogical University, ul. Mashinostroitelei 11, Yekaterinburg 620012, Russian Federation Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg 620990, Russian Federation Scopus Vereshchagin, V.P., Russian State Professional-Pedagogical University, ul. Mashinostroitelei 11, Yekaterinburg 620012, Russian Federation Subbotin, Y.N., Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg 620990, Russian Federation Chernykh, N.I., Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg 620990, Russian Federation WOS:000305481300018 000305481300018 |
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| Язык |
en
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| Права |
Restricted accedd (info:eu-repo/semantics/restrictedAccess)
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text/html
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| Охват |
RSVPU
SCOPUS |
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| Издатель |
Pleiades Publishing Ltd
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| Источник |
Proceedings of the Steklov Institute of Mathematics
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