24 citations · 53 across the 10 of their papers we have counts for
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Symmetries and exact solutions of a reaction-diffusion system arising in population dynamics
Philip Broadbridge, Roman Cherniha, Vasyl' Davydovych +1
A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible…
An age-structured diffusive model for epidemic modelling: Lie symmetries and exact solutions
Roman Cherniha, Vasyl' Davydovych
A new age-structured diffusive model for the mathematical modelling of epidemics is suggested. The model can be considered as a generalization of two models suggested earlier for t…
Analysis of a Mathematical Model for Fluid Transport in Poroelastic Materials in 2D Space
Roman Cherniha, Vasyl' Davydovych, Joanna Stachowska-Pietka +1
A mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the…
Symmetries and exact solutions of the diffusive Holling-Tanner prey-predator model
Roman Cherniha, Vasyl' Davydovych
We consider the classical Holling-Tanner model extended on 1D space by introducing the diffusion term. Making a reasonable simplification, the diffusive Holling-Tanner system is st…
The Shigesada-Kawasaki-Teramoto model: conditional symmetries, exact solutions and their properties
Roman Cherniha, Vasyl' Davydovych, John R. King
We study a simplification of the well-known Shigesada-Kawasaki-Teramoto model, which consists of two nonlinear reaction-diffusion equations with cross-diffusion. A complete set of…