Article
Ufa Mathematical Journal
Volume 4, Number 1, pp. 6-15
Equivalence group analysis and nonlinear self-adjointness of the generalized Kompaneets equation
Avdonina E.D., Ibragimov N.H.
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Equivalence group analysis is applied to the Kompaneets equation. We compute the equivalence Lie algebra for the corresponding \textit{generalized} Kompaneets equation. We also show that the generalized Kompaneets equation is nonlinearly self-adjoint.
The principle of an {\it a priori} use of symmetries gives a possibility to use the equivalence algebra in order to approximate the Kompaneets equation by an equation having a wider class of symmetries. Using an additional symmetry of the approximating equation and the nonlinear self-adjointness, one can construct new group invariant solutions and conservation laws.