Math. Model. Nat. Phenom.
Volume 6, Number 1, 2011Instability and patterns. Issue dedicated to the memory of A. Golovin
|Page(s)||138 - 148|
|Published online||09 June 2010|
Pattern Formation Induced by Time-Dependent Advection
Department of Physics, Humboldt University of Berlin,
Newtonstr. 15, D-12489,
2 Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany
* Corresponding author. E-mail:
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.
Mathematics Subject Classification: 35B36 / 35K57 / 92E20
Key words: pattern formation / reaction-advection-diffusion equation
© EDP Sciences, 2010
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