43 citations · 421 across the 43 of their papers we have counts for
43 papers
Lie symmetry classification and exact solutions of a diffusive Lotka-Volterra system with convection
Roman Cherniha, Vasyl' Davydovych
A mathematical model for description of the viscous fingering induced by a chemical reaction is under study. This complicated five-component model is reduced to a three-component d…
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…
Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems
Phillip Broadbridge, Roman Cherniha, Joanna Goard
New classes of conditionally integrable systems of nonlinear reaction-diffusion equations are introduced. They are obtained by extending a well known nonclassical symmetry of a sca…
A Mathematical Model for Two Solutes Transport in a Poroelastic Material and Its Applications
Roman Cherniha, Joanna Stachowska-Pietka, Jacek Waniewski
Using well-known mathematical foundations of the elasticity theory, a mathematical model for two solutes transport in a poroelastic material (soft tissue is a typical example) is s…