Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 112, pp. 115.
Lie group classification and exact solutions of
the generalized Kompaneets equations
Oleksii Patsiuk
Abstract:
We study generalized Kompaneets equations (GKEs) with one functional
parameter, and using the LieOvsiannikov algorithm, we carried out
the group classification. It is shown that the kernel algebra of the
full groups of the GKEs is the onedimensional Lie algebra.
Using the direct method, we find the equivalence group.
We obtain six nonequivalent (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 nonlinear 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.
Show me the PDF file (422 KB),
TEX file, and other files for this article.

Oleksii Patsiuk
Department of Partial differential equations
Institute of Mathematics
National Academy of Sciences of Ukraine
3 Tereshchenkivska Str., 01601 Kyiv4, Ukraine
email: patsyuck@yahoo.com Phone: +380995446899

Return to the EJDE web page