19 citations · 32 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★ 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…
math-ph2010
Lie Symmetries and Exact Solutions of the Generalized Thin Film Equation
Roman Cherniha, Phil Broadbridge, Liliia Myroniuk
A symmetry group classification for fourth-order reaction-diffusion equations, allowing for both second-order and fourth-order diffusion terms, is carried out. The fourth order equ…