29 citations · 73 across the 8 of their papers we have counts for
8 papers
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…
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…
Kinetics of the elementary act of electrochemical reactions at the semiconductor--electrolyte solution interface
Sergii Kovalenko, Veniamin Soloviev
In the framework of the quantum-mechanical theory of elementary act of non-adiabatic electrochemical reactions, it is carried out the calculation of the discharge current of ions a…
Exact solutions of nonlinear boundary value problems of the Stefan type
Roman Cherniha, Sergii Kovalenko
The (1+1)-dimensional nonlinear boundary value problem, modeling the process of melting and evaporation of metals, is studied by means of the classical Lie symmetry method. All pos…
Lie symmetry of a class of nonlinear boundary value problems with free boundaries
Roman Cherniha, Sergii Kovalenko
A class of (1+1)--dimensional nonlinear boundary value problems (BVPs), modeling the process of melting and evaporation of solid materials, is studied by means of the classical Lie…
Lie symmetries and reductions of multi-dimensional boundary value problems of the Stefan type
Roman Cherniha, Sergii Kovalenko
A new definition of Lie invariance for nonlinear multi-dimensional boundary value problems (BVPs) is proposed by the generalization of known definitions to much wider classes of BV…