Absence of Nontrivial Symmetries to the Heat Equation in Goursat Groups of Dimension at Least 4
- Authors: Kuznetsov M.V.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 60, No 1 (2019)
- Pages: 108-113
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172218
- DOI: https://doi.org/10.1134/S0037446619010129
- ID: 172218
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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).
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About the authors
M. V. Kuznetsov
Sobolev Institute of Mathematics
Author for correspondence.
Email: misha0123456789@mail.ru
Russian Federation, Novosibirsk