Electronic Journal of Differential Equations (Apr 2015)

Lie group classification and exact solutions of the generalized Kompaneets equations

  • Oleksii Patsiuk

Journal volume & issue
Vol. 2015, no. 112,
pp. 1 – 15

Abstract

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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.

Keywords