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: firstname.lastname@example.org Phone: +380995446899
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