Oleksii Patsiuk
Abstract:
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.
Submitted April 9, 2015. Published April 23, 2015.
Math Subject Classifications: 17B81, 35Q85, 35K10, 35K55.
Key Words: Generalized Kompaneets equation; group classification;
exact solution.
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Oleksii Patsiuk Department of Partial differential equations Institute of Mathematics National Academy of Sciences of Ukraine 3 Tereshchenkivska Str., 01601 Kyiv-4, Ukraine email: patsyuck@yahoo.com Phone: +380995446899 |
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