43 citations · 421 across the 43 of their papers we have counts for
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math-ph2010★ 29 cited
Lie symmetries of nonlinear boundary value problems
Roman Cherniha, Sergii Kovalenko
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of…
math-ph2010★ 26 cited
Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systems
Roman Cherniha
New definitions of -conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that diff…
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…