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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 3, Pages 39–49 (Mi ufa285)  

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.

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English version:
Ufa Mathematical Journal, 2015, 7:3, 38–46 (PDF, 349 kB); https://doi.org/10.13108/2015-7-3-38

Bibliographic databases:

UDC: 517.95
MSC: 35K70, 76M60
Received: 24.11.2014

Citation: V. V. Davydovych, “Preliminary group classification of $(2+1)$-dimensional linear ultraparabolic Kolmogorov–Fokker–Planck equations”, Ufimsk. Mat. Zh., 7:3 (2015), 39–49; Ufa Math. J., 7:3 (2015), 38–46

Citation in format AMSBIB
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