Autowave propagation for general reaction diffusion systems

Wave Motion ◽  
1993 ◽  
Vol 17 (3) ◽  
pp. 255-266 ◽  
Author(s):  
I.A. Molotkov ◽  
S.A. Vakulenko
Keyword(s):  
Reaction Diffusion ◽  
General Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Autowave Propagation

scholarly journals A review on symmetries for certain Aedes aegypti models

2015 ◽  
Vol 38 ◽  
pp. 1560073
Author(s):  
Igor Leite Freire ◽  
Mariano Torrisi
Keyword(s):  
Aedes Aegypti ◽  
Reaction Diffusion ◽  
Weak Equivalence ◽  
Invariant Solutions ◽  
General Reaction ◽  
Equivalence Transformations ◽  
Reaction Diffusion Systems ◽  
Group Invariant ◽  
Diffusion Systems ◽  
Group Invariant Solutions

We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.

TURING PATTERNS IN GENERAL REACTION-DIFFUSION SYSTEMS OF BRUSSELATOR TYPE

2010 ◽  
Vol 12 (04) ◽  
pp. 661-679 ◽  
Author(s):  
MARIUS GHERGU ◽  
VICENŢIU RĂDULESCU
Keyword(s):  
Chemical Reactions ◽  
Diffusion Coefficients ◽  
Crucial Role ◽  
Reaction Diffusion ◽  
Turing Patterns ◽  
General Reaction ◽  
Reaction Diffusion Systems ◽  
Brusselator Model ◽  
Diffusion Systems ◽  
Superlinear Growth

We study the reaction-diffusion system [Formula: see text] Here Ω is a smooth and bounded domain in ℝN (N ≥ 1), a, b, d1, d2 > 0 and f ∈ C1[0, ∞) is a non-decreasing function. The case f(u) = u2 corresponds to the standard Brusselator model for autocatalytic oscillating chemical reactions. Our analysis points out the crucial role played by the nonlinearity f in the existence of Turing patterns. More precisely, we show that if f has a sublinear growth then no Turing patterns occur, while if f has a superlinear growth then existence of such patterns is strongly related to the inter-dependence between the parameters a, b and the diffusion coefficients d1, d2.

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