期刊论文详细信息
Сибирский математический журнал | |
Absence of Nontrivial Symmetries to the Heat Equation in Goursat Groups of Dimension at Least 4 | |
M. V. Kuznetsov1  | |
[1] Sobolev Institute of Mathematics | |
关键词: sub-Laplacian; nilpotent Lie group; extension method; | |
DOI : 10.1134/S0037446619010129 | |
学科分类:数学(综合) | |
来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk | |
【 摘 要 】
Using the extension method, we study the one-parameter symmetry groups of the heat equation âtp = Îp, where \(\Delta=X_1^2+X_2^2\) is the sub-Laplacian constructed by a Goursat distribution span({X1, X2}) in ân, 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).
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO201910250703537ZK.pdf | 148KB | download |