109 citations · 372 across the 12 of their papers we have counts for
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math-ph2004★ 59 cited
Hierarchy of Conservation Laws of Diffusion--Convection Equations
Roman O. Popovych, Nataliya M. Ivanova
We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or s…
math-ph2004★ 7 cited
Conservation Laws and Potential Systems of Diffusion-Convection Equations
Nataliya M. Ivanova
We investigate conservation laws of diffusion-convection equations to construct first-order potential systems corresponding to these equations. We do two iterations of the construc…
math-ph2004★ 32 cited
Potential equivalence transformations for nonlinear diffusion-convection equations
Roman O. Popovych, Nataliya M. Ivanova
Potential equivalence transformations (PETs) are effectively applied to a class of nonlinear diffusion-convection equations. For this class all possible potential symmetries are cl…