Abstract:
In this paper we construct an optimal system of subalgebras for the nine-dimension Lie algebra of infinitesimal operators for a point symmetries group of a nonlinear heat equation with isotropic heat conductivity tensor and with a power dependence of the temperature. The results are presented as a lemma and a theorem. It is proven that up to transformations of internal automorphisms and some discrete automorphisms, there are 117 dissimilar subalgebras classes of various dimensions.
Keywords:
nonlinear heat equation, Lie algebra, optimal system of subalgebras.
Citation:
A. M. Ilyasov, “Optimal system of Lie algebra subalgebras of the point symmetries group for nonlinear heat equation without source”, Ufa Math. J., 5:3 (2013), 53–66
\Bibitem{Ily13}
\by A.~M.~Ilyasov
\paper Optimal system of Lie algebra subalgebras of the point symmetries group for nonlinear heat equation without source
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 3
\pages 53--66
\mathnet{http://mi.mathnet.ru/eng/ufa209}
\crossref{https://doi.org/10.13108/2013-5-3-53}
\elib{https://elibrary.ru/item.asp?id=20930800}
Linking options:
https://www.mathnet.ru/eng/ufa209
https://doi.org/10.13108/2013-5-3-53
https://www.mathnet.ru/eng/ufa/v5/i3/p54
This publication is cited in the following 2 articles:
R. K. Gazizov, A. A. Kasatkin, S. Yu. Lukashchuk, “Group classification and symmetry reduction of three-dimensional nonlinear anomalous diffusion equation”, Ufa Math. J., 11:4 (2019), 13–26
Citation in format AMSBIB
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