scholarly journals Non-linear reaction–diffusion systems with variable diffusivities: Lie symmetries, ansätze and exact solutions

2005 ◽  
Vol 308 (1) ◽  
pp. 11-35 ◽  
Author(s):  
Roman Cherniha ◽  
John R. King
Keyword(s):  
Exact Solutions ◽  
Reaction Diffusion ◽  
Lie Symmetries ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Linear Reaction ◽  
Non Linear

scholarly journals A reaction–diffusion system with cross-diffusion: Lie symmetry, exact solutions and their applications in the pandemic modelling

2021 ◽  
pp. 1-18
Author(s):  
ROMAN M. CHERNIHA ◽  
VASYL V. DAVYDOVYCH
Keyword(s):  
Exact Solutions ◽  
Reaction Diffusion ◽  
Interesting Case ◽  
Lie Symmetry ◽  
Point Of View ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems

A non-linear reaction–diffusion system with cross-diffusion describing the COVID-19 outbreak is studied using the Lie symmetry method. A complete Lie symmetry classification is derived and it is shown that the system with correctly specified parameters admits highly non-trivial Lie symmetry operators, which do not occur for all known reaction–diffusion systems. The symmetries obtained are also applied for finding exact solutions of the system in the most interesting case from applicability point of view. It is shown that the exact solutions derived possess typical properties for describing the pandemic spread under 1D approximation in space and lead to the distributions, which qualitatively correspond to the measured data of the COVID-19 spread in Ukraine.

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