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math-ph2014★ 4 cited
Lie symmetries of fundamental solutions of one (2+1)-dimensional ultra-parabolic Fokker--Planck--Kolmogorov equation
Sergii Kovalenko, Valeriy Stogniy, Maksym Tertychnyi
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 a…
math-ph2014★ 2 cited
Symmetry analysis and exact solutions of one class of (1+3)-dimensional boundary-value problems of the Stefan type
S. S. Kovalenko
We present the group classification of one class of (1+3)-dimensional nonlinear boundary-value problems of the Stefan type that simulate the processes of melting and evaporation of…
math-ph2012★ 1 cited
Group theoretic analysis of a class of boundary value problems for a nonlinear heat equation
Sergii Kovalenko
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wid…