Electron. J. Diff. Equ., Vol. 2015 (2015), No. 112, pp. 1-15.

Lie group classification and exact solutions of the generalized Kompaneets equations

Oleksii Patsiuk

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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