29 citations · 73 across the 8 of their papers we have counts for
4 papers · 1 filter
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…
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…