arXiv subjects

Valeriy Stogniy

Publications and source records attributed to Valeriy Stogniy.

2 recordsLinked to original sources

arXiv2018

Group classification of a class of generalized nonlinear Kolmogorov equations and exact solutions

A class of generalized nonlinear Kolmogorov equations is investigated. We present the group classification of Lie symmetries of the class with respect to the group of equivalence transformations. We find a number of exact solutions of nonlinear Kolmogorov equations which has the maximal symmetry properties.

math.AP↗

arXiv2014

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.

math-ph↗