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https://elar.rsvpu.ru/handle/123456789/28028
Название: | The Class of Solenoidal Planar-Helical Vector Fields |
Автор: | Vereshchagin, V. P. Subbotin, Y. N. Chernykh, N. I. |
Дата публикации: | 2011 |
Издатель: | Pleiades Publishing Ltd |
Аннотация: | 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. |
Ключевые слова: | CURL GROMEKA'S PROBLEM SCALAR FIELDS TENSOR FIELDS VECTOR FIELDS WAVELETS |
ISSN: | 0081-5438 1531-8605 |
DOI: | 10.1134/S008154381105018X |
SCOPUS: | 79959273501 |
WoS: | 000305481300018 |
Сведения о поддержке: | 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.” |
Располагается в коллекциях: | Научные публикации, проиндексированные в SCOPUS и WoS |
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