Nonlinear potential filtration equation and global actions of Lie symmetries
The Lie point symmetries of the nonlinear potential filtration equation break into five cases. Contact symmetries provide another two cases. By restricting to a natural class of functions, we show that these symmetries exponentiate to a global action of the corresponding Lie group in four of the...
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| Format: | Article |
| Language: | English |
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Texas State University
2009-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2009/101/abstr.html |
| _version_ | 1818482034768609280 |
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| author | Mark R. Sepanski |
| author_facet | Mark R. Sepanski |
| author_sort | Mark R. Sepanski |
| collection | DOAJ |
| description | The Lie point symmetries of the nonlinear potential filtration equation break into five cases. Contact symmetries provide another two cases. By restricting to a natural class of functions, we show that these symmetries exponentiate to a global action of the corresponding Lie group in four of the cases of Lie point symmetries. Furthermore, the action is actually the composition of a linear action with a simple translation. In fact, as a crucial step in applying the machinery of representation theory, this is accomplished using induced representations. In the remaining case as well as the contact symmetries, we show that the infinitesimal action does not exponentiate to any global Lie group action on any reasonable space of functions. |
| first_indexed | 2024-12-10T11:42:56Z |
| format | Article |
| id | doaj.art-7e54ab89b9cc4ef48b7e71494488a4f3 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T11:42:56Z |
| publishDate | 2009-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-7e54ab89b9cc4ef48b7e71494488a4f32022-12-22T01:50:11ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912009-08-012009101,124Nonlinear potential filtration equation and global actions of Lie symmetriesMark R. SepanskiThe Lie point symmetries of the nonlinear potential filtration equation break into five cases. Contact symmetries provide another two cases. By restricting to a natural class of functions, we show that these symmetries exponentiate to a global action of the corresponding Lie group in four of the cases of Lie point symmetries. Furthermore, the action is actually the composition of a linear action with a simple translation. In fact, as a crucial step in applying the machinery of representation theory, this is accomplished using induced representations. In the remaining case as well as the contact symmetries, we show that the infinitesimal action does not exponentiate to any global Lie group action on any reasonable space of functions.http://ejde.math.txstate.edu/Volumes/2009/101/abstr.htmlLie symmetrynonlinear potential filtration equationglobal action |
| spellingShingle | Mark R. Sepanski Nonlinear potential filtration equation and global actions of Lie symmetries Electronic Journal of Differential Equations Lie symmetry nonlinear potential filtration equation global action |
| title | Nonlinear potential filtration equation and global actions of Lie symmetries |
| title_full | Nonlinear potential filtration equation and global actions of Lie symmetries |
| title_fullStr | Nonlinear potential filtration equation and global actions of Lie symmetries |
| title_full_unstemmed | Nonlinear potential filtration equation and global actions of Lie symmetries |
| title_short | Nonlinear potential filtration equation and global actions of Lie symmetries |
| title_sort | nonlinear potential filtration equation and global actions of lie symmetries |
| topic | Lie symmetry nonlinear potential filtration equation global action |
| url | http://ejde.math.txstate.edu/Volumes/2009/101/abstr.html |
| work_keys_str_mv | AT markrsepanski nonlinearpotentialfiltrationequationandglobalactionsofliesymmetries |