Nonnegative solutions to reaction–diffusion system with cross‐diffusion and nonstandard growth conditions

2020 ◽  
Vol 43 (10) ◽  
pp. 6576-6597
Author(s):  
Gurusamy Arumugam ◽  
Jagmohan Tyagi
Keyword(s):  
Reaction Diffusion ◽  
Growth Conditions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Cross Diffusion ◽  
Nonstandard Growth ◽  
Nonnegative Solutions ◽  
Nonstandard Growth Conditions

Unique continuation for a reaction-diffusion system with cross diffusion

2019 ◽  
Vol 27 (4) ◽  
pp. 511-525 ◽  
Author(s):  
Bin Wu ◽  
Ying Gao ◽  
Zewen Wang ◽  
Qun Chen
Keyword(s):  
Unique Continuation ◽  
Reaction Diffusion ◽  
Cauchy Data ◽  
Carleman Estimate ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Lateral Boundary ◽  
Strongly Coupled ◽  
Cross Diffusion ◽  
Coupled Reaction

Abstract This paper concerns unique continuation for a reaction-diffusion system with cross diffusion, which is a drug war reaction-diffusion system describing a simple dynamic model of a drug epidemic in an idealized community. We first establish a Carleman estimate for this strongly coupled reaction-diffusion system. Then we apply the Carleman estimate to prove the unique continuation, which means that the Cauchy data on any lateral boundary determine the solution uniquely in the whole domain.

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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