Ufa Mathematical Journal
    Volume 5, Number 3, pp. 53-66

    Optimal system of Lie algebra subalgebras of point symmetries group for nonlinear heat equation without source

    Ilyasov A.M.


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    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.