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Turing instability of anomalous reaction–anomalous diffusion systems

Published online by Cambridge University Press:  01 June 2008

Y. NEC  and
A. A. NEPOMNYASHCHY
Y. NEC
Affiliation:
Department of Mathematics, Technion, Israel Institute of Technology, Haifa, Israel email: flyby@techunix.technion.ac.il, nepom@techunix.technion.ac.il
A. A. NEPOMNYASHCHY
Affiliation:
Department of Mathematics, Technion, Israel Institute of Technology, Haifa, Israel email: flyby@techunix.technion.ac.il, nepom@techunix.technion.ac.il
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Abstract

Linear stability theory is developed for an activator–inhibitor model where fractional derivative operators of generally different exponents act both on diffusion and reaction terms. It is shown that in the short wave limit the growth rate is a power law of the wave number with decoupled time scales for distinct anomaly exponents of the different species. With equal anomaly exponents an exact formula for the anomalous critical value of reactants diffusion coefficients' ratio is obtained.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 19 , Issue 3 , June 2008 , pp. 329 - 349
Copyright
Copyright © Cambridge University Press 2008

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