scholarly journals CROSS-DIFFUSION INDUCED INSTABILITY AND STABILITY IN REACTION-DIFFUSION SYSTEMS

2011 ◽  
Vol 1 (1) ◽  
pp. 95-119 ◽  
Author(s):  
Junping Shi ◽  
◽  
Zhifu Xie ◽  
Kristina Little ◽  
◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems

Turing space in reaction-diffusion systems with density-dependent cross diffusion

2013 ◽  
Vol 87 (3) ◽  
Author(s):  
E. P. Zemskov ◽  
K. Kassner ◽  
M. J. B. Hauser ◽  
W. Horsthemke
Keyword(s):  
Reaction Diffusion ◽  
Density Dependent ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems

Instability induced by cross-diffusion in reaction–diffusion systems

2010 ◽  
Vol 11 (2) ◽  
pp. 1036-1045 ◽  
Author(s):  
Canrong Tian ◽  
Zhigui Lin ◽  
Michael Pedersen
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems

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.

scholarly journals Stationary reaction–diffusion systems in L1

2018 ◽  
Vol 28 (11) ◽  
pp. 2161-2190 ◽  
Author(s):  
El Haj Laamri ◽  
Michel Pierre
Keyword(s):  
Chemical Reactions ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Systems Modeling ◽  
Main Difficulty ◽  
Accretive Operators ◽  
Abstract Result ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems

We prove existence of solutions to stationary [Formula: see text] reaction–diffusion systems where the data are in [Formula: see text] or in [Formula: see text]. We first give an abstract result where the “diffusions” are nonlinear [Formula: see text]-accretive operators in [Formula: see text] and the reactive terms are assumed to satisfy [Formula: see text] structural inequalities. It implies that the situation is controlled by an associated cross-diffusion system and provides [Formula: see text]-estimates on the reactive terms. Next we prove existence for specific systems modeling chemical reactions and which naturally satisfy less than [Formula: see text] structural (in)equalities. The main difficulty is also to obtain [Formula: see text]-estimates on the nonlinear reactive terms.

Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations

2014 ◽  
Vol 70 (4) ◽  
pp. 709-743 ◽  
Author(s):  
Anotida Madzvamuse ◽  
Hussaini S. Ndakwo ◽  
Raquel Barreira
Keyword(s):  
Systems Analysis ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems
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