19 citations · 37 across the 3 of their papers we have counts for
3 papers
math-ph2012★ 19 cited
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…
math-ph2012★ 5 cited
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…
math-ph2012★ 13 cited
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…