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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| Format: | Article |
| Language: | English |
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Texas State University
2015-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/112/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |