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Siberian Mathematical Journal

, Volume 60, Issue 1, pp 108–113 | Cite as

Absence of Nontrivial Symmetries to the Heat Equation in Goursat Groups of Dimension at Least 4

  • M. V. KuznetsovEmail author
Article
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Abstract

Using the extension method, we study the one-parameter symmetry groups of the heat equation ∂tp = Δp, where \(\Delta=X_1^2+X_2^2\) is the sub-Laplacian constructed by a Goursat distribution span({X1, X2}) in ℝn, where the vector fields X1 and X2 satisfy the commutation relations [X1, Xj] = Xj+1 (where Xn+1 = 0) and [Xj, Xk] = 0 for j ≥ 1 and k ≥ 1. We show that there are no such groups for n ≥ 4 (with exception of the linear transformations of solutions which are admitted by every linear equation).

Keywords

sub-Laplacian nilpotent Lie group extension method 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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