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

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.

preprint2014arXivOpen access
Sergii KovalenkoValeriy StogniyMaksym Tertychnyi
math.APmath-phmath.MP
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Sergii KovalenkoValeriy StogniyMaksym Tertychnyi

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