Lie group classification and exact solutions of the generalized Kompaneets equations
We study generalized Kompaneets equations (GKEs) with one functional parameter, and using the Lie-Ovsiannikov algorithm, we carried out the group classification. It is shown that the kernel algebra of the full groups of the GKEs is the one-dimensional Lie algebra. Using the direct method, we fin...
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Texas State University
2015-04-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/112/abstr.html |
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doaj-9d4f49fe69034bfeaa09ce9017535a952020-11-24T22:44:24ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-04-012015112,115Lie group classification and exact solutions of the generalized Kompaneets equationsOleksii Patsiuk0 National Academy of Sciences, Ukraine We study generalized Kompaneets equations (GKEs) with one functional parameter, and using the Lie-Ovsiannikov algorithm, we carried out the group classification. It is shown that the kernel algebra of the full groups of the GKEs is the one-dimensional Lie algebra. Using the direct method, we find the equivalence group. We obtain six non-equivalent (up to transformations from the equivalence group) GKEs that allow wider invariance algebras than the kernel one. We find a number of exact solutions of the non-linear GKE which has the maximal symmetry properties.http://ejde.math.txstate.edu/Volumes/2015/112/abstr.htmlGeneralized Kompaneets equationgroup classificationexact solution |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Oleksii Patsiuk |
| spellingShingle |
Oleksii Patsiuk Lie group classification and exact solutions of the generalized Kompaneets equations Electronic Journal of Differential Equations Generalized Kompaneets equation group classification exact solution |
| author_facet |
Oleksii Patsiuk |
| author_sort |
Oleksii Patsiuk |
| title |
Lie group classification and exact solutions of the generalized Kompaneets equations |
| title_short |
Lie group classification and exact solutions of the generalized Kompaneets equations |
| title_full |
Lie group classification and exact solutions of the generalized Kompaneets equations |
| title_fullStr |
Lie group classification and exact solutions of the generalized Kompaneets equations |
| title_full_unstemmed |
Lie group classification and exact solutions of the generalized Kompaneets equations |
| title_sort |
lie group classification and exact solutions of the generalized kompaneets equations |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2015-04-01 |
| description |
We study generalized Kompaneets equations (GKEs) with one functional
parameter, and using the Lie-Ovsiannikov algorithm, we carried out
the group classification. It is shown that the kernel algebra of the
full groups of the GKEs is the one-dimensional Lie algebra.
Using the direct method, we find the equivalence group.
We obtain six non-equivalent (up to transformations from the equivalence
group) GKEs that allow wider invariance algebras than the kernel one.
We find a number of exact solutions of the non-linear GKE which
has the maximal symmetry properties. |
| topic |
Generalized Kompaneets equation group classification exact solution |
| url |
http://ejde.math.txstate.edu/Volumes/2015/112/abstr.html |
| work_keys_str_mv |
AT oleksiipatsiuk liegroupclassificationandexactsolutionsofthegeneralizedkompaneetsequations |
| _version_ |
1725691883475173376 |