Lie symmetries of fundamental solutions of one (2+1)-dimensional ultra-parabolic Fokker--Planck--Kolmogorov equation

2014/08/01 by Sergii Kovalenko, Kovalenko, Sergii, Valeriy Stogniy +3
Mathematics · Physics and Astronomy · #22E70 #35K70 #35Q84 #Advanced Mathematical Physics Problems #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1408.0166

openalex publication_date 2014/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A (2+1)-dimensional linear ultra-parabolic Fokker--Planck--Kolmogorov equation is investigated from the group-theoretical point of view. By using the Berest--Aksenov approach, an algebra of invariance of fundamental solutions of the equation is found. A fundamental solution of the equation under study is computed in an explicit form as a weak invariant solution.

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