This article is cited in 4 papers

Preliminary group classification of $(2+1)$-dimensional linear ultraparabolic Kolmogorov–Fokker–Planck equations

V. V. Davydovych

Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, Ukraine

Abstract: We make a preliminary group classification of a class of $(2+1)$-dimensional ultraparabolic equations invariant under low-dimensional solvable Lie algebras. It is shown that there exist one, six and four nonequivalent ultraparabolic equations admitting two-, three-, and four-dimensional solvable Lie algebras, respectively.

Keywords: ultraparabolic equation, equivalence transformation, group classification, maximal invariance algebra, solvable Lie algebra.

UDC: 517.95

MSC: 35K70, 76M60

Received: 24.11.2014

 English version: Ufa Mathematical Journal, 2015, 7:3, 38–46

Bibliographic databases:

• 
• 
•