Journal
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
Volume 6, Issue 1, Pages 138-148Publisher
EDP SCIENCES S A
DOI: 10.1051/mmnp/20116107
Keywords
pattern formation; reaction-advection-diffusion equation
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Funding
- German Science Foundation, DFG [SPP 1164, STR 1021/1-2]
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We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators, and show that a mixing advection can lead to a pattern-forming instability in a two-component system where only one of the species is advected. Physically, this can be explained as crossing a threshold of Turing instability due to effective increase of one of the diffusion constants.
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